A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam br...A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.展开更多
In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable...In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable system parameter conditions. Codimension-two bifurcations of the discrete epidemic model, associated with 1：1 strong resonance, 1：2 strong resonance, 1：3 strong resonance and 1：4 strong resonance, are analyzed by using the bifurcation theorem and the normal form method of maps. Moreover, in order to eliminate the chaotic behavior of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations are obtained by the phase portraits, the maximum Lyapunov exponents diagrams for two different varying parameters in 3-dimension space, the bifurcation diagrams, the computations of Lyapunov exponents and the dynamic response. They not only illustrate the validity of the proposed results, but also display the interesting and complex dynamical behaviors.展开更多
We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portrai...We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.展开更多
As a typical biochemical reaction, the process of continuous fermentation of ethanol is studied in this paper. An improved model is set forward and in agreement with experiments. Nonlinear oscillations of the process ...As a typical biochemical reaction, the process of continuous fermentation of ethanol is studied in this paper. An improved model is set forward and in agreement with experiments. Nonlinear oscillations of the process are analyzed with analytical and numerical methods. The Hopf bifurcation region is fixed and further analyses are given.展开更多
The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is stu...The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.展开更多
The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method...The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.展开更多
Local bifurcation phenomena in a four-dlmensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the b...Local bifurcation phenomena in a four-dlmensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.展开更多
A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map...A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.展开更多
This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms,and with linear delayed velocity feedback.The analysis indicates that for a sufficiently large velocity feedback gain,th...This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms,and with linear delayed velocity feedback.The analysis indicates that for a sufficiently large velocity feedback gain,the equilibrium of the system may undergo a number of stability switches with an increase of time delay,and then becomes unstable forever.At each critical value of time delay for which the system changes its stability,a generic Hopf bifurcation occurs and a periodic motion emerges in a one-sided neighbourhood of the critical time delay.The method of Fredholm alternative is applied to determine the bifurcating periodic motions and their stability.It stresses on the effect of the system parameters on the stable regions and the amplitudes of the bifurcating periodic solutions.展开更多
This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is fur...This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called “time-2τ^2 map” of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T^1 （Hopf invariant circles）, tori 2T^1 and tori 2T^2 depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms＇ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.展开更多
The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The...The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.展开更多
To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control va...To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control variable of Chay model based on simulation results. The procedure of period adding bifurcation scenario from period k to period k ＋ 1 bursting （k = 1, 2, 3, 4） involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map. Moreover, dynamics of the border-collision bifurcation is identified in the discontinuous map, which is employed to understand the experimentally observed period increment sequence. The simple discontinuous map is of practical importance in modeling of collective behaviours of neural populations like synchronization in large neural circuits.展开更多
This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end....This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.展开更多
The jump and bifurcation of Duffing oscillator with hardening spring subject to narrow-band random excitation are systematically and comprehensively examined. It is shown that, in a certain domain of the space of the ...The jump and bifurcation of Duffing oscillator with hardening spring subject to narrow-band random excitation are systematically and comprehensively examined. It is shown that, in a certain domain of the space of the oscillator and excitation parameters, there are two types of more probable motions in the stationary response of the Duffing oscillator and jumps may occur. The jump is a transition of the response from one more probable motion to another or vise versa. Outside the domain the stationary response is either nearly Gaussian or like a diffused limit cycle. As the parameters change across the boundary of the domain the qualitative behavior of the stationary response changes and it is a special kind of bifurcation. It is also shown that, for a set of specified parameters, the statistics are unique and they are independent of initial condition. It is pointed out that some previous results and interpretations on this problem are incorrect.展开更多
Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristi...Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristic of the nonlin- ear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set, and then the bifurcation dia- grams in different persistent regions are obtained.展开更多
In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter va...In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.展开更多
In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights o...In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights on bifurcation and stability, also obtain some conditions for subcfitical and supercritical. Finally, we give some numerical simulation studies of system in order to verify analytic results.展开更多
AIM:To explore the anatomical relationships between bronchial artery and tracheal bifurcation using computed tomography angiography (CTA).METHODS:One hundred consecutive patients (84 men,16 women;aged 46-85 years) who...AIM:To explore the anatomical relationships between bronchial artery and tracheal bifurcation using computed tomography angiography (CTA).METHODS:One hundred consecutive patients (84 men,16 women;aged 46-85 years) who underwent CTA using multi-detector row CT (MDCT) were investigated retrospectively.The distance between sites of bronchial artery ostia and tracheal bifurcation,and dividing directions were explored.The directions of division from the descending aorta were described as on a clock face.RESULTS:We identified ostia of 198 bronchial arteries:95 right bronchial arteries,67 left bronchial arteries,36 common trunk arteries.Of these,172 (87%) divided from the descending aorta,25 (13%) from the aortic arch,and 1 (0.5%) from the left subclavian artery.The right,left,and common trunk bronchial arteries divided at-1 to 2 cm from tracheal bifurcation with frequencies of 77% (73/95),82% (54/66),and 70% (25/36),respectively.The dividing direction of right bronchial arteries from the descending aorta was 9 to 10 o’clock with a frequency of 81% (64/79);that of left and common tract bronchial arteries was 11 to 1 o’clock with frequencies of 70% (43/62) and 77% (24/31),respectively.CONCLUSION:CTA using MDCT provides details of the relation between bronchial artery ostia and tracheal bifurcation.展开更多
The present paper deals with a singular nonlinear boundary value problem arising in the theory of power law fluids, sufficient conditions for the existence of bifurcation solutions to the problem are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11002093,11172183,and 11202142)the Science and Technology Fund of the Science and Technology Department of Hebei Province,China(Grant No.11215643)
文摘A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 60974004 and 71001074, and the Science Research Foundation of Department of Education of Liaoning Province of China under Grant No. W2010302.
文摘In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable system parameter conditions. Codimension-two bifurcations of the discrete epidemic model, associated with 1：1 strong resonance, 1：2 strong resonance, 1：3 strong resonance and 1：4 strong resonance, are analyzed by using the bifurcation theorem and the normal form method of maps. Moreover, in order to eliminate the chaotic behavior of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations are obtained by the phase portraits, the maximum Lyapunov exponents diagrams for two different varying parameters in 3-dimension space, the bifurcation diagrams, the computations of Lyapunov exponents and the dynamic response. They not only illustrate the validity of the proposed results, but also display the interesting and complex dynamical behaviors.
基金supported by the National Natural Science Foundations of China(12371171)and the Natural Science Foundation of Jiangsu Province(BK20221339).
文摘We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.
文摘As a typical biochemical reaction, the process of continuous fermentation of ethanol is studied in this paper. An improved model is set forward and in agreement with experiments. Nonlinear oscillations of the process are analyzed with analytical and numerical methods. The Hopf bifurcation region is fixed and further analyses are given.
文摘The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.
文摘The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.
基金supported by the National Natural Science Foundation of China (Grant Nos 60774088,10772135 and 60574036)the Research Foundation from the Ministry of Education of China (Grant Nos 107024 and 207005)+1 种基金the Program for New Century Excellent Talents in University of China (NCET)the Application Base and Frontier Technology Project of Tianjin,China(Grant No 08JCZDJC21900)
文摘Local bifurcation phenomena in a four-dlmensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.
基金The project supported by the National Natural Scicnce Foundation of China(10172042,50475109)the Natural Science Foundation of Gansu Province Government of China(ZS-031-A25-007-Z(key item))
文摘A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.
基金The project supported by the National Natural Science Foundation of China (19972025)
文摘This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms,and with linear delayed velocity feedback.The analysis indicates that for a sufficiently large velocity feedback gain,the equilibrium of the system may undergo a number of stability switches with an increase of time delay,and then becomes unstable forever.At each critical value of time delay for which the system changes its stability,a generic Hopf bifurcation occurs and a periodic motion emerges in a one-sided neighbourhood of the critical time delay.The method of Fredholm alternative is applied to determine the bifurcating periodic motions and their stability.It stresses on the effect of the system parameters on the stable regions and the amplitudes of the bifurcating periodic solutions.
基金The project supported by the Nutional Natural Science Foundation of China(10472096)
文摘This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called “time-2τ^2 map” of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T^1 （Hopf invariant circles）, tori 2T^1 and tori 2T^2 depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms＇ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.
基金supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10774088,10772101,30770701 and 10875076)the Fundamental Research Funds for the Central Universities(Grant No.GK200902025)
文摘To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control variable of Chay model based on simulation results. The procedure of period adding bifurcation scenario from period k to period k ＋ 1 bursting （k = 1, 2, 3, 4） involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map. Moreover, dynamics of the border-collision bifurcation is identified in the discontinuous map, which is employed to understand the experimentally observed period increment sequence. The simple discontinuous map is of practical importance in modeling of collective behaviours of neural populations like synchronization in large neural circuits.
基金The project supported by the Science Foundation of Tongji UniversityNational Key Projects of China under Grant No.PD9521907
文摘This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.
基金The project supported by National Natural Science Foundation of China
文摘The jump and bifurcation of Duffing oscillator with hardening spring subject to narrow-band random excitation are systematically and comprehensively examined. It is shown that, in a certain domain of the space of the oscillator and excitation parameters, there are two types of more probable motions in the stationary response of the Duffing oscillator and jumps may occur. The jump is a transition of the response from one more probable motion to another or vise versa. Outside the domain the stationary response is either nearly Gaussian or like a diffused limit cycle. As the parameters change across the boundary of the domain the qualitative behavior of the stationary response changes and it is a special kind of bifurcation. It is also shown that, for a set of specified parameters, the statistics are unique and they are independent of initial condition. It is pointed out that some previous results and interpretations on this problem are incorrect.
基金supported by the National Natural Science Foundation of China(10632040)
文摘Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristic of the nonlin- ear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set, and then the bifurcation dia- grams in different persistent regions are obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.10772135 and 60874028)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11202148)+2 种基金the Incentive Funding of the National Research Foundation of South Africa(GrantNo.IFR2009090800049)the Eskom Tertiary Education Support Programme of South Africathe Research Foundation of Tianjin University of Science and Technology
文摘In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.
文摘In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights on bifurcation and stability, also obtain some conditions for subcfitical and supercritical. Finally, we give some numerical simulation studies of system in order to verify analytic results.
文摘AIM:To explore the anatomical relationships between bronchial artery and tracheal bifurcation using computed tomography angiography (CTA).METHODS:One hundred consecutive patients (84 men,16 women;aged 46-85 years) who underwent CTA using multi-detector row CT (MDCT) were investigated retrospectively.The distance between sites of bronchial artery ostia and tracheal bifurcation,and dividing directions were explored.The directions of division from the descending aorta were described as on a clock face.RESULTS:We identified ostia of 198 bronchial arteries:95 right bronchial arteries,67 left bronchial arteries,36 common trunk arteries.Of these,172 (87%) divided from the descending aorta,25 (13%) from the aortic arch,and 1 (0.5%) from the left subclavian artery.The right,left,and common trunk bronchial arteries divided at-1 to 2 cm from tracheal bifurcation with frequencies of 77% (73/95),82% (54/66),and 70% (25/36),respectively.The dividing direction of right bronchial arteries from the descending aorta was 9 to 10 o’clock with a frequency of 81% (64/79);that of left and common tract bronchial arteries was 11 to 1 o’clock with frequencies of 70% (43/62) and 77% (24/31),respectively.CONCLUSION:CTA using MDCT provides details of the relation between bronchial artery ostia and tracheal bifurcation.
文摘The present paper deals with a singular nonlinear boundary value problem arising in the theory of power law fluids, sufficient conditions for the existence of bifurcation solutions to the problem are obtained.
