We focus on the hysteretic characteristics of the varying compliance(VC) principal resonance in a ball bearing. The branches of the periodic VC response are traced by the harmonic balance method and the alternating fr...We focus on the hysteretic characteristics of the varying compliance(VC) principal resonance in a ball bearing. The branches of the periodic VC response are traced by the harmonic balance method and the alternating frequency/time domain technique(HB-AFT) embedding Arc-length continuation, and the stability of these solutions is investigated by using Floquet theory. We find that the resonant response displays a swallow-tail structure due to the coupling nonlinearities between the Hertzian contact and the bearing clearance, which differs from the soft hysteresis of the non-loss Hertzian contact resonances. Furthermore, we find that period-1 VC branch cannot completely characterize the response of the system for a large bearing clearance, because multiple instability regions may occur from the cyclic fold, the secondary Hopf bifurcations, supercritical and subcritical period doubling bifurcations, in which case co-existences of period-1, period-2, and even quasi-periodic VC motions emerge in the hysteretic resonant range.展开更多
The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibr...The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.展开更多
In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In th...In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.展开更多
In this paper,a distributed consensus protocol is proposed for discrete-time single-integer multi-agent systems with measurement noises under general fixed directed topologies.The time-varying control gains satisfying...In this paper,a distributed consensus protocol is proposed for discrete-time single-integer multi-agent systems with measurement noises under general fixed directed topologies.The time-varying control gains satisfying the stochastic approximation conditions are introduced to attenuate noises,thus the closed-loop multi-agent system is intrinsically a linear time-varying stochastic difference system.Then the mean square consensus convergence analysis is developed based on the Lyapunov technique,and the construction of the Lyapunov function especially does not require the typical balanced network topology condition assumed for the existence of quadratic Lyapunov function.Thus,the proposed consensus protocol can be applicable to more general networked multi-agent systems,particularly when the bidirectional and/or balanced information exchanges between agents are not required.Under the proposed protocol,it is proved that the state of each agent converges in mean square to a common random variable whose mathematical expectation is the weighted average of agents' initial state values;meanwhile,the random variable's variance is bounded.展开更多
An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the ...An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the diseasefree equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.展开更多
In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with di...In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with different edges on transmission rate as epidemics prevail. Furthermore, by constructing Lyapunov function, we prove that the disease-free equilibrium E^0 is globally asymptotically stable as the epidemic threshold R^＊〈 1. When R^＊ 〉 1, we obtain the permanence of epidemic and the local stability of endemic equilibrium E＊. Finally, one can find a good agreement between numerical simulations and our analytical results.展开更多
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2015CB057400)the China Postdoctoral Science Foundation(Grant No.2013M541360)the National Natural Science Foundation of China(Grant Nos.10632040 and 11302058)
文摘We focus on the hysteretic characteristics of the varying compliance(VC) principal resonance in a ball bearing. The branches of the periodic VC response are traced by the harmonic balance method and the alternating frequency/time domain technique(HB-AFT) embedding Arc-length continuation, and the stability of these solutions is investigated by using Floquet theory. We find that the resonant response displays a swallow-tail structure due to the coupling nonlinearities between the Hertzian contact and the bearing clearance, which differs from the soft hysteresis of the non-loss Hertzian contact resonances. Furthermore, we find that period-1 VC branch cannot completely characterize the response of the system for a large bearing clearance, because multiple instability regions may occur from the cyclic fold, the secondary Hopf bifurcations, supercritical and subcritical period doubling bifurcations, in which case co-existences of period-1, period-2, and even quasi-periodic VC motions emerge in the hysteretic resonant range.
文摘The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.
文摘In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.
基金supported by the Natural Science Foundation of China under Grant Nos.61073101,61073102,61170172,61272153,and 61374176the Science Fund for Creative Research Groups of the National Natural Science Foundation of China under Grant No.61221003Anhui Provincial Natural Science Foundation under Grant No.090412251
文摘In this paper,a distributed consensus protocol is proposed for discrete-time single-integer multi-agent systems with measurement noises under general fixed directed topologies.The time-varying control gains satisfying the stochastic approximation conditions are introduced to attenuate noises,thus the closed-loop multi-agent system is intrinsically a linear time-varying stochastic difference system.Then the mean square consensus convergence analysis is developed based on the Lyapunov technique,and the construction of the Lyapunov function especially does not require the typical balanced network topology condition assumed for the existence of quadratic Lyapunov function.Thus,the proposed consensus protocol can be applicable to more general networked multi-agent systems,particularly when the bidirectional and/or balanced information exchanges between agents are not required.Under the proposed protocol,it is proved that the state of each agent converges in mean square to a common random variable whose mathematical expectation is the weighted average of agents' initial state values;meanwhile,the random variable's variance is bounded.
文摘An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the diseasefree equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.
基金This work is supported by the National Natural Science Foundation of China under Grant 61174039. The authors would like to thank the editor and the reviewers for their constructive comments and suggestions to improve the quality of this paper.
文摘In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with different edges on transmission rate as epidemics prevail. Furthermore, by constructing Lyapunov function, we prove that the disease-free equilibrium E^0 is globally asymptotically stable as the epidemic threshold R^＊〈 1. When R^＊ 〉 1, we obtain the permanence of epidemic and the local stability of endemic equilibrium E＊. Finally, one can find a good agreement between numerical simulations and our analytical results.
