Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently so...Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.展开更多
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
A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positi...A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positive solution.Second,by selecting an appropriate Lyapunov function,we provide the sufficient condition for the existence of a positive T-periodic solution.Finally,numerical simulations illustrate our theoretical results,which show that the impulse or the white noises can result in the extinction of the predator in a certain condition.展开更多
In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave so...In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.展开更多
In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is als...In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.展开更多
This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol...In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.展开更多
Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkho...Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results.展开更多
One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equati...One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.展开更多
The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As a...The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.展开更多
Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m ...Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.展开更多
In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q...In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q d x 2 d t=x 2Q m 2x 1/Qk 2+x 1/Q-x 2.It is proved that the system is exist at least one stable periodic solution on under the following condition:m 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2】m 1δk 1(k 2+Q 2λ 2) 2.Furthermore, ifm 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2【m 1δk 1(k 2-Q 2λ 2) 2mold true them equilibrium point (s *,x * 1,x * 2)∈ set Ω is global asymptotic stable.展开更多
Aim To discuss the existence of periodic solutions for the first boundary problem of incompressible non Newtonian fluids, a problem arising from polymer processing and concerned with the first initial boundary valu...Aim To discuss the existence of periodic solutions for the first boundary problem of incompressible non Newtonian fluids, a problem arising from polymer processing and concerned with the first initial boundary value problem of nonstationary flow of the non Newtonian viscous incompressible fluids through slit dice. Methods The monotone operator theory and Schauders fixed point theorem were used. Results and Conclusion The existence theorem of periodic solutions of a Dirichlet problem is proved under reasonable conditions.展开更多
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ...The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.展开更多
Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set ...Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.展开更多
J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
Energy access remains a critical challenge in rural South Sudan,with communities heavily relying on expensive and unfriendly environmental energy sources such as diesel generators and biomass.This study addresses the ...Energy access remains a critical challenge in rural South Sudan,with communities heavily relying on expensive and unfriendly environmental energy sources such as diesel generators and biomass.This study addresses the predicament by evaluating the feasibility of renewable energy-based decentralized electrification in the selected village ofDoleibHill,UpperNile,South Sudan.Using a demand assessment and theMulti-Tier Framework(MTF)approach,it categorizes households,public facilities,private sector,Non-GovernmentalOrganizations(NGOs)and business energy needs and designs an optimized hybrid energy system incorporating solar Photovoltaic(PV),wind turbines,batteries,and a generator.The proposed system,simulated in Hybrid Optimization Model Electric Renewable(HOMER)Pro,demonstrates strong economic viability,with a present worth of$292,145,an annual worth of$22,854,a return on investment(ROI)of 36.5%,and an internal rate of return(IRR)of 42.1%.The simple payback period is 2.31 years,and the discounted payback period is 2.62 years.The system achieves a levelized cost of energy(LCOE)of$0.276/kWh and significantly reduces dependence on diesel,producing 798,800 kWh annually fromwind energy.This research provides a replicable model for cost-effective,sustainable rural electrification,offering valuable insights for policymakers and energy planners seeking to expand electricity access in off-grid communities.展开更多
In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabili...In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.展开更多
基金Supported by NSFC (No.12371378)NSF of Fujian Province (Nos.2024J01980,2023J01955)。
文摘Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.
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 NSFC(Nos.10671182,12061020)NSF of Guizhou Province(Nos.QKH[2019]1123,QKHKY[2021]088,QKHKY[2022]301,QKH-ZK[2021]331)the Ph.D.Project of Guizhou Education University(No.2021BS005)。
文摘A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positive solution.Second,by selecting an appropriate Lyapunov function,we provide the sufficient condition for the existence of a positive T-periodic solution.Finally,numerical simulations illustrate our theoretical results,which show that the impulse or the white noises can result in the extinction of the predator in a certain condition.
基金Supported by the National Natural Science Foundation of China(12261050)Science and Technology Project of Department of Education of Jiangxi Province(GJJ2201612 and GJJ211027)Natural Science Foundation of Jiangxi Province of China(20212BAB202021)。
文摘In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.
基金Supported by the National Natural Science Foundation of China(12171247)。
文摘In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.
文摘Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results.
文摘One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.
文摘The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.
文摘Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.
文摘In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q d x 2 d t=x 2Q m 2x 1/Qk 2+x 1/Q-x 2.It is proved that the system is exist at least one stable periodic solution on under the following condition:m 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2】m 1δk 1(k 2+Q 2λ 2) 2.Furthermore, ifm 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2【m 1δk 1(k 2-Q 2λ 2) 2mold true them equilibrium point (s *,x * 1,x * 2)∈ set Ω is global asymptotic stable.
文摘Aim To discuss the existence of periodic solutions for the first boundary problem of incompressible non Newtonian fluids, a problem arising from polymer processing and concerned with the first initial boundary value problem of nonstationary flow of the non Newtonian viscous incompressible fluids through slit dice. Methods The monotone operator theory and Schauders fixed point theorem were used. Results and Conclusion The existence theorem of periodic solutions of a Dirichlet problem is proved under reasonable conditions.
文摘The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.
文摘Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.
文摘J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
文摘Energy access remains a critical challenge in rural South Sudan,with communities heavily relying on expensive and unfriendly environmental energy sources such as diesel generators and biomass.This study addresses the predicament by evaluating the feasibility of renewable energy-based decentralized electrification in the selected village ofDoleibHill,UpperNile,South Sudan.Using a demand assessment and theMulti-Tier Framework(MTF)approach,it categorizes households,public facilities,private sector,Non-GovernmentalOrganizations(NGOs)and business energy needs and designs an optimized hybrid energy system incorporating solar Photovoltaic(PV),wind turbines,batteries,and a generator.The proposed system,simulated in Hybrid Optimization Model Electric Renewable(HOMER)Pro,demonstrates strong economic viability,with a present worth of$292,145,an annual worth of$22,854,a return on investment(ROI)of 36.5%,and an internal rate of return(IRR)of 42.1%.The simple payback period is 2.31 years,and the discounted payback period is 2.62 years.The system achieves a levelized cost of energy(LCOE)of$0.276/kWh and significantly reduces dependence on diesel,producing 798,800 kWh annually fromwind energy.This research provides a replicable model for cost-effective,sustainable rural electrification,offering valuable insights for policymakers and energy planners seeking to expand electricity access in off-grid communities.
基金supported by Social Science Fund of Hunan province(Grant No.22JD074)the Research Foundation of Education Bureau of Hunan province(Grant No.22B0912).
文摘In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.
