The Lengyel–Epstein reaction–diffusion system of the CIMA reaction is revisited. We construct a Lyapunov function to show that the constant equilibrium solution is globally asymptotically stable when the feeding rate of iodide is small. We also show that for small spatial domains, all solutions eventually converge to a spatially homogeneous and timeperiodic solution. © 2008 Elsevier Ltd. All ri...

It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predatorprey system, we show that the solution curve of the limit cycle exhibits temporal patterns of a relaxation oscillator, or a Heaviside function, when certain parameter is small.

This paper investigates projective synchronization with time delay and parameter mismatch for a lately proposed simple yet complex one-parameter chaotic system, and Rössler system as well. With an active control scheme, it is proved that the zero solution of the dynamical error system is globally asymptotically stable based on Barbalat’s lemma. Numerical simulations verify the correctness and e...

x(n + 1) : x(n)exp Jr (n ) (1 x(n) K(n) ] J ' where {r(n)} and {K(n)} are positive w-periodic sequences. Sufficient conditions are obtained for the existence of a positive and globally asymptotically stable w-periodic solution. Counterexamples are given to illustrate that the conclusions in [1] are incorrect. (~) 2003 Elsevier Science Ltd. All rights reserved.

We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for fully nonlinear GAC systems with actuator errors are also discussed.

We announce a new construction of a stabilizing feedback law for nonlinear globally asymptotically controllable (GAC) systems. Given a control affine GAC system, our feedback renders the closed loop system input to state stable with respect to actuator errors and small observation noise. We also announce a variant of our result for fully nonlinear GAC systems.

The nonlinear feedback cascade model of the underactuated IWP is obtained through a collocated partial feedback linearization and a global change of coordinates. A nonlinear controller is designed with the nonlinear recursive technology. The system stability is proved with Lyapunov theory. The simulation results show the system is globally asymptotically stable to the origin.

The main concern of this paper is to study the dynamics of an n-dimensional ratio-dependent predator-prey system with diffusion. We study the dissipativeness, persistence of the system and it is shown that the unique positive constant steady state is globally asymptotically stable under some assumptions.

A delayed predator-prey model with diffusion and competition is proposed. Some sufficient conditions on uniform persistence of the model have been obtained. By applying LiapunovRazumikhin technique, we will point out, under almost periodic circumstances, a set of sufficient conditions that assure the existence and uniqueness of the positive almost periodic solution which is globally asymptotica...

It was conjectured that for every integer m 3 the unique equilibrium c = 1 of the generalized Putnam equation xn+1 = ∑m−2 i=0 xn−i + xn−m+1xn−m xnxn−1 + ∑m i=2 xn−i , n= 0,1,2, . . . , with positive initial conditions is globally asymptotically stable. In this paper, we prove this conjecture. © 2005 Elsevier Inc. All rights reserved.