Controlling Chaos in Neuron Based on Lasalle Invariance Principle

A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalleinvariant principle.The control technique does not require analytical knowledge of the system dynamics and operateswithout an explicit knowledge of the desired steady-state position.The well-known modified Hodgkin-Huxley (MHH)and Hindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method.Simulationresults show the proposed control law is effective.The outcome of this study is significant since it is helpful to understandthe learning process of a human brain towards the information processing,memory and abnormal discharge of the brainneurons.

Stability of switched nonlinear systems via extensions of LaSalle's invariance principle

This paper studies the extension of LaSalle＇s invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle＇s invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.

Cluster consensus of second-order multi-agent systems via pinning control

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

Hybrid Synchronization of Fractional-Order Complex Networks Model via Fractional Order Controller

For the purpose of investigating two complex networks' hybrid synchronization,a controller with fractional-order is provided.Regarding hybrid synchronization which includes the outer synchronization and inner synchronization,some hybrid synchronization's sufficient conditions according to the Lyapunov stability theorem and the LaSalle invariance principle are proposed.Theoretical analysis suggests that,only when the state of driving-response networks is outer synchronization and each network is in inner synchronization,two coupled networks' hybrid synchronization under some suitable conditions could be reached.Finally,theoretical results are illustrated and validated with the given numerical simulations.

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

This paper studies the asymptotic behavior of solutions for nonlinear RLCnetwoiks which have the following form The function p i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditiolts. Under the assumption that every element value involving voltage source is asymptotically constallt, we establish four creteria for all solutiolls of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited uonliltear circuits.This results generalize those of Brayton and Moser[1,2].

Stability and Hopf Bifurcation of a Virus Infection Model with a Delayed CTL Immune Response

In this paper, a virus infection model with standard incidence rate and delayed CTL immune response is investigated. By analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the CTL-activated infection equilibrium are established, respectively. By means of comparison arguments, it is verified that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio is less than unity. By using suitable Lyapunov functional and LaSalle's invariance principle, it is shown that the CTL-inactivated infection equilibrium of the system is globally asymptotically stable if the immune response reproduction ratio is less than unity and the basic reproduction ratio is greater than unity. Numerical simulations are carried out to illustrate the theoretical result.

Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake and a time delay

In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are car- ried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equi- librium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium E＋ is obtained. Numerical simulations are also performed to illustrate the results.

GLOBAL DYNAMICS OF A DELAYED HIV-1 INFECTION MODEL WITH ABSORPTION AND SATURATION INFECTION

In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle＇s invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.

Distributed cooperative formation of multiple mobile agents with preserved connectivity

This paper investigates distributed cooperative formation control of a group of multiple mobile agents with a virtual leader,where information exchange among agents is modeled by the group topology,and the states of the virtual leader are known only by parts of the agents.We develop a class of distributed formation control laws with similar form.The steered group is proved to achieve the desired formation objectives as long as the intersection of the initial communication topology and the formation goal topology is connected.This requirement of connectivity can be easily achieved by many practical applications;consequently,our developed distributed control laws are effective and feasible.Furthermore,for the developed control laws,we show the influence of different information flow graph of agents on the convergence rate and robustness to node and connection failures.

Traveling wave solutions for a diffusive predator-prey model with predator saturation and competition

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.