Many predator–prey systems with oscillatory behavior possess a unique limit cycle which is globally asymptotically stable. For a class of general predator–prey system, we show that the solution orbit of the limit cycle exhibits the temporal pattern of a relaxation oscillator, when a certain parameter is small. 2014 Elsevier Inc. All rights reserved.

We extend results of Gouzé and Hadeler (in Nonlinear World 1:23-34, 1994) concerning the dynamics generated by a map on an ordered metric space that can be decomposed into increasing and decreasing parts. Our main results provide sufficient conditions for the existence of a globally asymptotically stable fixed point for the map. Applications to discrete-time, stage-structured population models ...

In this paper, we consider a delayed diffusive Leslie–Gower predator–prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexist...

This paper presents a converse Lyapunov theorem for discrete-time systems with disturbances taking values in compact sets. Among several new stability results, it is shown that a smooth Lyapunov function exists for a family of time-varying discrete systems if these systems are robustly globally asymptotically stable. c © 2002 Elsevier Science B.V. All rights reserved.

This paper studies the problem of controlling chaos in Lorenz system. By dividing Lorenz system into two subsystems, the small gain theorem is used to design linear feedback controllers to make the equilibrium points of the controlled system globally asymptotically stable. Thus chaos in Lorenz system disappears under the controller.

Explicit formulas of smooth time-varying state feedbacks, which make the origin of an underactuated surface vessel globally uniformly asymptotically stable, are proposed. The construction of the feedback extensively relies on the backstepping approach. The feedbacks constructed are time-periodic functions.

It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predator-prey 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. MSC 2000: 34C26, 34C15, 34C07, 92D25

This paper deals with the tracking control problem of flexible joint robots under the assumption that the link and robot positions are the only measured signals. A globally asymptotically stable state feedback controller and a nonlinear observer is proposed which guarantees the semiglobal asymptotic tracking of the system obtained by the designed dynamic output feedback controller. Examples ill...

In this work, an economic growth model with endogenous labor shift under a dual economy is given. It is proved that the model has unique nonzero equilibrium and its solution is globally asymptotically stable, and the aggregate capital growth of the industrial sector and the labor shift appear in eight different patterns at different initial conditions. c © 2007 Elsevier Ltd. All rights reserved.

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 inputto-state stable (ISS) with respect to actuator errors. Extensions for fully nonlinear GAC systems with actuator errors are also discussed. Our controllers have the property that they tolerate small observation noise as...