This paper studies a non-reciprocal swarm model that consists of a group of mobile autonomous agents with an attraction-repulsion function governing the interaction of the agents. The function is chosen to have infini...This paper studies a non-reciprocal swarm model that consists of a group of mobile autonomous agents with an attraction-repulsion function governing the interaction of the agents. The function is chosen to have infinitely large values of repulsion for vanishing distance between two agents so as to avoid occurrence of collision. It is shown analytically that under the detailed balance condition in coupling weights, all the agents will aggregate and eventually form a cohesive cluster of finite size around the weighted center of the swarm in a finite time. Moreover, the swarm system is completely stable, namely, the motion of all agents converge to the set of equilibrium points. For the general case of non-reciprocal swarms without the detailed balance condition, numerical simulations show that more complex self-organized oscillations can emerge in the swarms. The effect of noise on collective dynamics of the swarm is also examined with a white Gaussian noise model.展开更多
The existence, uniqueness, globally exponential stability andspeed of exponential convergence for a class of cellular neural networks are investigated. The existence of a unique equilibrium is proved under very concis...The existence, uniqueness, globally exponential stability andspeed of exponential convergence for a class of cellular neural networks are investigated. The existence of a unique equilibrium is proved under very concise conditions, and theorems for estimating the global convergence speed approaching the equilibrium and criteria for its globally exponential stability are derived, Considering synapse time delay, by constructing appropriate Lyapunov functional, the existence of a unique equilibrium and its global stability for the delayed network are also proved. The results, which do not require the cloning template to be symmetric, are easy to use in network design.展开更多
基金supported by the National Natural Science Foundation of China (No.60674047, 60674050, 60528007)National 863 Program (No.2006AA04Z247,2006AA04Z258)+2 种基金11-5 project (No.A2120061303)SRFDP (No.20060001013)the Doctoral Fund and Youth Key Fund of North China University of Technology
文摘This paper studies a non-reciprocal swarm model that consists of a group of mobile autonomous agents with an attraction-repulsion function governing the interaction of the agents. The function is chosen to have infinitely large values of repulsion for vanishing distance between two agents so as to avoid occurrence of collision. It is shown analytically that under the detailed balance condition in coupling weights, all the agents will aggregate and eventually form a cohesive cluster of finite size around the weighted center of the swarm in a finite time. Moreover, the swarm system is completely stable, namely, the motion of all agents converge to the set of equilibrium points. For the general case of non-reciprocal swarms without the detailed balance condition, numerical simulations show that more complex self-organized oscillations can emerge in the swarms. The effect of noise on collective dynamics of the swarm is also examined with a white Gaussian noise model.
基金This work was supported by the National Natural Science Foundation of China ( Grant No. 69871005) .
文摘The existence, uniqueness, globally exponential stability andspeed of exponential convergence for a class of cellular neural networks are investigated. The existence of a unique equilibrium is proved under very concise conditions, and theorems for estimating the global convergence speed approaching the equilibrium and criteria for its globally exponential stability are derived, Considering synapse time delay, by constructing appropriate Lyapunov functional, the existence of a unique equilibrium and its global stability for the delayed network are also proved. The results, which do not require the cloning template to be symmetric, are easy to use in network design.
