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 operateswi...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.展开更多
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...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.展开更多
We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logari...We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.展开更多
Let {Xn} be a sequence of i.i.d.r. v. s with mean 0 and variance 1, Sn = ∑i=1nXi- Suppose H(x)】0 (x≥0) is a non-decreasing continuous function such that for some γ】0 and x0】0, x-2-γ(x)(x≥x0) is non-decreasing ...Let {Xn} be a sequence of i.i.d.r. v. s with mean 0 and variance 1, Sn = ∑i=1nXi- Suppose H(x)】0 (x≥0) is a non-decreasing continuous function such that for some γ】0 and x0】0, x-2-γ(x)(x≥x0) is non-decreasing and x -1logH(x) (x≥x0) is non-increasing. If x-1 logH(x)→0 (x→∞), then Sn - W(n)=o (invH(n)) a.s. (n → ∞) holds if and only if EH(t|X1|)【∞ for all t】0.展开更多
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 ...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.展开更多
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 equilibr...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.展开更多
In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s i...In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.展开更多
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 t...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].展开更多
By developing the mechanical proving method, we determine the structure of LaSalle’sinvariant set for 7-dimensional Lotka-Volterra food chain systems, based on Ritt-Wu’s prin-ciple. We then further show that the loc...By developing the mechanical proving method, we determine the structure of LaSalle’sinvariant set for 7-dimensional Lotka-Volterra food chain systems, based on Ritt-Wu’s prin-ciple. We then further show that the locally asymptotical stable equilibrium point of Lotka-Volterra food chain systems for 7 dimension must be globally stable.展开更多
Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed...Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed to deal with the singular problem. However, the issue of numerical instability and high computational complexity has not found a satisfactory solution so far. In this paper, we consider the singular optimization problem with bounded variables constraint rather than the common unconstraint model. A novel neural network model was proposed for solving the problem of singular convex optimization with bounded variables. Under the assumption of rank one defect, the original difficult problem is transformed into nonsingular constrained optimization problem by enforcing a tensor term. By using the augmented Lagrangian method and the projection technique, it is proven that the proposed continuous model is convergent to the solution of the singular optimization problem. Numerical simulation further confirmed the effectiveness of the proposed neural network approach.展开更多
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 sync...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.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10862001 and 10947011the Construction of Key Laboratories in Universities of Guangxi under Grant No. 200912
文摘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.
基金Supported partly by the National Natural Science Foundation of China (Grant Nos. 60221301, 60674022 and 60736022)
文摘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.
基金This research supported by Grants from the National Natural Science Foundation of China(No.11225104)and the Fundamental Research Funds for the Central Universities.
文摘We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.
基金Project supported by the National Natural Science Foundation of China.
文摘Let {Xn} be a sequence of i.i.d.r. v. s with mean 0 and variance 1, Sn = ∑i=1nXi- Suppose H(x)】0 (x≥0) is a non-decreasing continuous function such that for some γ】0 and x0】0, x-2-γ(x)(x≥x0) is non-decreasing and x -1logH(x) (x≥x0) is non-increasing. If x-1 logH(x)→0 (x→∞), then Sn - W(n)=o (invH(n)) a.s. (n → ∞) holds if and only if EH(t|X1|)【∞ for all t】0.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70571059)
文摘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.
基金Supported by the NNSF of China(11371368,11071254)Supported by the NSF of Hebei Province(A2014506015)Supported by the NSF for Young Scientists of Hebei Province(A2013506012)
文摘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.
基金This work was supported by the National Natural Science Foundation of China(No.11371368)and(No.11871316)。
文摘In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.
文摘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].
基金Project supported by the National Natural Science Foundation of China.
文摘By developing the mechanical proving method, we determine the structure of LaSalle’sinvariant set for 7-dimensional Lotka-Volterra food chain systems, based on Ritt-Wu’s prin-ciple. We then further show that the locally asymptotical stable equilibrium point of Lotka-Volterra food chain systems for 7 dimension must be globally stable.
文摘Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed to deal with the singular problem. However, the issue of numerical instability and high computational complexity has not found a satisfactory solution so far. In this paper, we consider the singular optimization problem with bounded variables constraint rather than the common unconstraint model. A novel neural network model was proposed for solving the problem of singular convex optimization with bounded variables. Under the assumption of rank one defect, the original difficult problem is transformed into nonsingular constrained optimization problem by enforcing a tensor term. By using the augmented Lagrangian method and the projection technique, it is proven that the proposed continuous model is convergent to the solution of the singular optimization problem. Numerical simulation further confirmed the effectiveness of the proposed neural network approach.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61201227)the Funding of China Scholarship Council,the Natural Science Foundation of Anhui Province(Grant No.1208085MF93)the 211 Innovation Team of Anhui University(Grant Nos.KJTD007A and KJTD001B)
文摘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.
