The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding sto...The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.展开更多
Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimati...Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.展开更多
In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theo...In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.展开更多
Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are stud...Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are studied based on properties of Gammma distributions. Some p-moment exponential stability of the solutions are given.展开更多
Isolationism and expansionism are two themes of American diplomacy. From the beginning of the state’s history, isolationism and expansionism have manifested themselves as two policy imperatives in American diplomacy....Isolationism and expansionism are two themes of American diplomacy. From the beginning of the state’s history, isolationism and expansionism have manifested themselves as two policy imperatives in American diplomacy. On the surface, isolationism and expansionism represent contradictory attitudes and assumptions about America’s proper relationship with the outside world: isolationism advocates diplomatic and military non-entanglement in world affairs; expansionism urges active involvement in external affairs. But in a deeper sense, both isolationism and expansionism are manifestations of American sense of mission, the belief that the US has a special role to perform for all nations in the world. Isolationism is a passive approach to accomplish that mission: it emphasizes the exemplary nature of their country. Expansionism stresses the need for active involvement to achieve that mission; thus, is an active approach to American mission.展开更多
Hearing loss is a common military health problem and it is closely related to exposures to impulse noises from blast explosions and weapon firings. In a study based on test data of chinchillas and scaled to humans (Mi...Hearing loss is a common military health problem and it is closely related to exposures to impulse noises from blast explosions and weapon firings. In a study based on test data of chinchillas and scaled to humans (Military Medicine, 181: 59-69), an empirical injury model was constructed for exposure to multiple sound impulses of equal intensity. Building upon the empirical injury model, we conduct a mathematical study of the hearing loss injury caused by multiple impulses of non-uniform intensities. We adopt the theoretical framework of viewing individual sound exposures as separate injury causing events, and in that framework, we examine synergy for causing injury (fatigue) or negative synergy (immunity) or independence among a sequence of doses. Starting with the empirical logistic dose-response relation and the empirical dose combination rule, we show that for causing injury, a sequence of sound exposure events are not independent of each other. The phenomenological effect of a preceding event on the subsequent event is always immunity. We extend the empirical dose combination rule, which is applicable only in the case of homogeneous impulses of equal intensity, to accommodate the general case of multiple heterogeneous sound exposures with non-uniform intensities. In addition to studying and extending the empirical dose combination rule, we also explore the dose combination rule for the hypothetical case of independent events, and compare it with the empirical one. We measure the effect of immunity quantitatively using the immunity factor defined as the percentage of decrease in injury probability attributed to the sound exposure in the preceding event. Our main findings on the immunity factor are: 1) the immunity factor is primarily a function of the difference in SELA (A- weighted sound exposure level) between the two sound exposure events;it is virtually independent of the magnitude of the two SELA values as long as the difference is fixed;2) the immunity factor increases monotonically from 0 to 100% as the first dose is varied from being significantly below the second dose, to being moderately above the second dose. The extended dose-response formulation developed in this study provides a theoretical framework for assessing the injury risk in realistic situations.展开更多
In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are e...In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.展开更多
We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crow...We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crowd vs the effective combined dose follows the logistic dose-response relation. The injury risk of a crowd is the average fraction of injured. The injury risk was measured in experiments as follows: each subject is individually exposed to a sequence of acoustic impulses of a given intensity and the injury is recorded;results of multiple individual subjects were assembled into data sets to mimic the response of a crowd. The effective combined dose was adjusted by varying the number of impulses in the sequence. The most prominent feature observed in experiments is that the injury risk of the crowd caused by multiple impulses is significantly less than the value predicted based on assumption that all impulses act independently in causing injury and all subjects in the crowd are statistically identical. Previously, in the case where all subjects are statistically identical (i.e., no biovariability), we interpreted the observed injury risk caused by multiple impulses in terms of the immunity effects of preceding impulses on subsequent impulses. In this study, we focus on the case where all sound exposure events act independently in causing injury regardless of whether one is preceded by another (i.e., no immunity effect). Instead, we explore the possibility of interpreting the observed logistic dose-response relation in the framework of biovariability of the crowd. Here biovariability means that subjects in the crowd have their own individual injury probabilities. That is, some subjects are biologically less or more susceptible to hearing loss injury than others. We derive analytically the distribution of individual injury probability that produces the observed logistic dose-response relation. For several parameter values, we prove that the derived distribution is mathematically a proper density function. We further study the asymptotic approximations for the density function and discuss their significance in practical numerical computation with finite precision arithmetic. Our mathematical analysis implies that the observed logistic dose-response relation can be theoretically explained in the framework of biovariability in the absence of immunity effect.展开更多
The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The f...The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.展开更多
The results of research on influence of an irradiation of a liquid phase by nanosecond electromagnetic impulses(NEMI) on processes of crystallization and structurization,physicomechanical and operational properties of...The results of research on influence of an irradiation of a liquid phase by nanosecond electromagnetic impulses(NEMI) on processes of crystallization and structurization,physicomechanical and operational properties of copper,aluminium and alloys on their basis(bronze and silumin) were presented.展开更多
A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (in finitely many) state-dependent in pulses on the right-hand side. This appr...A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (in finitely many) state-dependent in pulses on the right-hand side. This approach gives a natural numerical scheme to approximate the solution.The convergence of the approximation is proved and its asymptatic order obtained.展开更多
A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are pr...A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.展开更多
The basic concept of this research is to analyse the approximate controllability(AC)of a nonlinear delay integrodifferential evolution system(NDIDES) with random impulse of the type■by assuming that the linear system...The basic concept of this research is to analyse the approximate controllability(AC)of a nonlinear delay integrodifferential evolution system(NDIDES) with random impulse of the type■by assuming that the linear system is approximately controllable. The existence and uniqueness of the mild solution to above system have been determined by using the Banach contraction principle and trajectory accessible sets. We generalize the results for NDIDES with and without fixed-type impulsive moments.展开更多
Considering the mutual interference between species, a stochastic predator-prey model with impulses and Holling-II functional response is proposed in this paper. Firstly, by constructing an equivalent system without i...Considering the mutual interference between species, a stochastic predator-prey model with impulses and Holling-II functional response is proposed in this paper. Firstly, by constructing an equivalent system without impulses, the existence of a globally unique positive solution is proved. Secondly, in cases of the mutual coefficient m = 1 and 0 m < 1, by constructing suitable Lyapunov functional, the existence of T-periodic solution is investigated under some certain conditions. Finally, numerical simulation is introduced to verify our main results.展开更多
This paper will add to an evolving new paradigm for financial decision-making by exploring the important roles that intuition, heuristics, and impulses play as a bridge between how the conscious and unconscious can wo...This paper will add to an evolving new paradigm for financial decision-making by exploring the important roles that intuition, heuristics, and impulses play as a bridge between how the conscious and unconscious can work together more effectively in making better decisions. Historically, the roles of financial/accounting theory and cognitive psychology have been extensively studied and documented in attempting to explain individual financial decision-making. More recently, neuroscience has made substantial contributions to learning how prospective financial decisions and outcomes affect brain activity and observed decision-making behavior. The evidence from neuroscience indicates that up to 90% of our decisions are initiated at the unconscious level, which is only beginning to be investigated in a systematic manner. Integrating these findings from multiple disciplines, including recent contributions from neuroscience, has many implications, not only with respect to personal and corporate financial decisions and how markets work, but also as an essential component in the tool box of the general decision maker.展开更多
For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbation...For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.展开更多
In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, ...In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov function and using comparison theorem with an impulsive differential equation, we study that a positive periodic solution exists. Thirdly, we prove that system is globally attractive. Finally, numerical simulations are presented to show the feasibility of the obtained results.展开更多
In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of po...In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and generalize the known ones in [1], as an application, we also give an example to illustrate the feasibility of our main results.展开更多
Neurologists define the transmission of nerve impulses across the membranes of the neural cells as a result of difference in the concentration of ions while they measured an electric potential, called as an action pot...Neurologists define the transmission of nerve impulses across the membranes of the neural cells as a result of difference in the concentration of ions while they measured an electric potential, called as an action potential, which allows the propagation of such nerve impulses as electrical signals. Such measurements should guide them to a logical explanation of the nerve impulses as electric charges driven by the measured action potential. However, such logical conclusion, or explanation, is ignored due to a wrong definition of the flow of electric charges as a flow of electrons that cannot pass through neural networks. According to recent studies, electric charges are properly defined as electromagnetic (EM) waves whose energy is expressed as the product of its propagating electric potential times their entropy flow which is adhered to the flow of such energy. Such definition matches the logical conclusion of the nerve impulses as electric charges, as previously explained, and defines the entropy of the neural network, measured by Ammeters, in Watt or Joule/Volt. The measured entropy represents a neurodiagnostic property of the neural networks that measures its capacity to allow the flow of energy per unit action potential. Theoretical verification of the innovative definition of nerve impulses is presented by following an advanced entropy approach. A proper review of the machine records of the stimulating electric charges, used in the diagnosis of the neural networks, and the stimulated nerve impulses or stimulated responses, represents practical verifications of the innovative definitions of the electric charges and the nerve impulses. Comparing the functioning of the thermoelectric generators and the brain neurons, such neurons are defined as thermoelectric generators of the electric nerve impulses and their propagating, or action, potential.展开更多
In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,.....In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).展开更多
基金Supported by the National Natural Science Foundation of China(10671182)。
文摘The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.
基金supported by the National Natural Science Foundation of China(61833005)
文摘Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.
基金Supported by Shandong University of Finance and Economics 2023 International Collaborative Projectsthe National Natural Science Foundation of China(Grant No.62073190)。
文摘In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.
基金partially supported by Fund Scientific Research MU15FMIIT008,Plovdiv University
文摘Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are studied based on properties of Gammma distributions. Some p-moment exponential stability of the solutions are given.
文摘Isolationism and expansionism are two themes of American diplomacy. From the beginning of the state’s history, isolationism and expansionism have manifested themselves as two policy imperatives in American diplomacy. On the surface, isolationism and expansionism represent contradictory attitudes and assumptions about America’s proper relationship with the outside world: isolationism advocates diplomatic and military non-entanglement in world affairs; expansionism urges active involvement in external affairs. But in a deeper sense, both isolationism and expansionism are manifestations of American sense of mission, the belief that the US has a special role to perform for all nations in the world. Isolationism is a passive approach to accomplish that mission: it emphasizes the exemplary nature of their country. Expansionism stresses the need for active involvement to achieve that mission; thus, is an active approach to American mission.
文摘Hearing loss is a common military health problem and it is closely related to exposures to impulse noises from blast explosions and weapon firings. In a study based on test data of chinchillas and scaled to humans (Military Medicine, 181: 59-69), an empirical injury model was constructed for exposure to multiple sound impulses of equal intensity. Building upon the empirical injury model, we conduct a mathematical study of the hearing loss injury caused by multiple impulses of non-uniform intensities. We adopt the theoretical framework of viewing individual sound exposures as separate injury causing events, and in that framework, we examine synergy for causing injury (fatigue) or negative synergy (immunity) or independence among a sequence of doses. Starting with the empirical logistic dose-response relation and the empirical dose combination rule, we show that for causing injury, a sequence of sound exposure events are not independent of each other. The phenomenological effect of a preceding event on the subsequent event is always immunity. We extend the empirical dose combination rule, which is applicable only in the case of homogeneous impulses of equal intensity, to accommodate the general case of multiple heterogeneous sound exposures with non-uniform intensities. In addition to studying and extending the empirical dose combination rule, we also explore the dose combination rule for the hypothetical case of independent events, and compare it with the empirical one. We measure the effect of immunity quantitatively using the immunity factor defined as the percentage of decrease in injury probability attributed to the sound exposure in the preceding event. Our main findings on the immunity factor are: 1) the immunity factor is primarily a function of the difference in SELA (A- weighted sound exposure level) between the two sound exposure events;it is virtually independent of the magnitude of the two SELA values as long as the difference is fixed;2) the immunity factor increases monotonically from 0 to 100% as the first dose is varied from being significantly below the second dose, to being moderately above the second dose. The extended dose-response formulation developed in this study provides a theoretical framework for assessing the injury risk in realistic situations.
文摘In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.
文摘We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crowd vs the effective combined dose follows the logistic dose-response relation. The injury risk of a crowd is the average fraction of injured. The injury risk was measured in experiments as follows: each subject is individually exposed to a sequence of acoustic impulses of a given intensity and the injury is recorded;results of multiple individual subjects were assembled into data sets to mimic the response of a crowd. The effective combined dose was adjusted by varying the number of impulses in the sequence. The most prominent feature observed in experiments is that the injury risk of the crowd caused by multiple impulses is significantly less than the value predicted based on assumption that all impulses act independently in causing injury and all subjects in the crowd are statistically identical. Previously, in the case where all subjects are statistically identical (i.e., no biovariability), we interpreted the observed injury risk caused by multiple impulses in terms of the immunity effects of preceding impulses on subsequent impulses. In this study, we focus on the case where all sound exposure events act independently in causing injury regardless of whether one is preceded by another (i.e., no immunity effect). Instead, we explore the possibility of interpreting the observed logistic dose-response relation in the framework of biovariability of the crowd. Here biovariability means that subjects in the crowd have their own individual injury probabilities. That is, some subjects are biologically less or more susceptible to hearing loss injury than others. We derive analytically the distribution of individual injury probability that produces the observed logistic dose-response relation. For several parameter values, we prove that the derived distribution is mathematically a proper density function. We further study the asymptotic approximations for the density function and discuss their significance in practical numerical computation with finite precision arithmetic. Our mathematical analysis implies that the observed logistic dose-response relation can be theoretically explained in the framework of biovariability in the absence of immunity effect.
基金National Natural Science Foundations of China(No.11601143,11801160)School Level Scientific Research Project of Hunan First Normal University,China(No.XYS14N15)
文摘The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.
基金This work is financially supported by Program of Russian Foundation For Basic Research(No 05-08-01357)
文摘The results of research on influence of an irradiation of a liquid phase by nanosecond electromagnetic impulses(NEMI) on processes of crystallization and structurization,physicomechanical and operational properties of copper,aluminium and alloys on their basis(bronze and silumin) were presented.
文摘A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (in finitely many) state-dependent in pulses on the right-hand side. This approach gives a natural numerical scheme to approximate the solution.The convergence of the approximation is proved and its asymptatic order obtained.
基金The Special Research Funds for Young Col-lege Teacher of Shanghai (No. 355877)
文摘A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.
文摘The basic concept of this research is to analyse the approximate controllability(AC)of a nonlinear delay integrodifferential evolution system(NDIDES) with random impulse of the type■by assuming that the linear system is approximately controllable. The existence and uniqueness of the mild solution to above system have been determined by using the Banach contraction principle and trajectory accessible sets. We generalize the results for NDIDES with and without fixed-type impulsive moments.
文摘Considering the mutual interference between species, a stochastic predator-prey model with impulses and Holling-II functional response is proposed in this paper. Firstly, by constructing an equivalent system without impulses, the existence of a globally unique positive solution is proved. Secondly, in cases of the mutual coefficient m = 1 and 0 m < 1, by constructing suitable Lyapunov functional, the existence of T-periodic solution is investigated under some certain conditions. Finally, numerical simulation is introduced to verify our main results.
文摘This paper will add to an evolving new paradigm for financial decision-making by exploring the important roles that intuition, heuristics, and impulses play as a bridge between how the conscious and unconscious can work together more effectively in making better decisions. Historically, the roles of financial/accounting theory and cognitive psychology have been extensively studied and documented in attempting to explain individual financial decision-making. More recently, neuroscience has made substantial contributions to learning how prospective financial decisions and outcomes affect brain activity and observed decision-making behavior. The evidence from neuroscience indicates that up to 90% of our decisions are initiated at the unconscious level, which is only beginning to be investigated in a systematic manner. Integrating these findings from multiple disciplines, including recent contributions from neuroscience, has many implications, not only with respect to personal and corporate financial decisions and how markets work, but also as an essential component in the tool box of the general decision maker.
文摘For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.
文摘In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov function and using comparison theorem with an impulsive differential equation, we study that a positive periodic solution exists. Thirdly, we prove that system is globally attractive. Finally, numerical simulations are presented to show the feasibility of the obtained results.
文摘In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and generalize the known ones in [1], as an application, we also give an example to illustrate the feasibility of our main results.
文摘Neurologists define the transmission of nerve impulses across the membranes of the neural cells as a result of difference in the concentration of ions while they measured an electric potential, called as an action potential, which allows the propagation of such nerve impulses as electrical signals. Such measurements should guide them to a logical explanation of the nerve impulses as electric charges driven by the measured action potential. However, such logical conclusion, or explanation, is ignored due to a wrong definition of the flow of electric charges as a flow of electrons that cannot pass through neural networks. According to recent studies, electric charges are properly defined as electromagnetic (EM) waves whose energy is expressed as the product of its propagating electric potential times their entropy flow which is adhered to the flow of such energy. Such definition matches the logical conclusion of the nerve impulses as electric charges, as previously explained, and defines the entropy of the neural network, measured by Ammeters, in Watt or Joule/Volt. The measured entropy represents a neurodiagnostic property of the neural networks that measures its capacity to allow the flow of energy per unit action potential. Theoretical verification of the innovative definition of nerve impulses is presented by following an advanced entropy approach. A proper review of the machine records of the stimulating electric charges, used in the diagnosis of the neural networks, and the stimulated nerve impulses or stimulated responses, represents practical verifications of the innovative definitions of the electric charges and the nerve impulses. Comparing the functioning of the thermoelectric generators and the brain neurons, such neurons are defined as thermoelectric generators of the electric nerve impulses and their propagating, or action, potential.
文摘In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).
