We investigate a class of multigroup dengue epidemic model. We show that the global dynamics are determined by the basic reproductive number R0. We present that when R0 ≤ 1, there is a unique disease-free equilibrium which is globally asymptotically stable; when R0 > 1, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the...

A general discrete juvenile-adult population model with time-dependent birth rate and nonlinear survivorship rates is studied. When breeding is continuous, it is shown that the model has a unique globally asymptotically stable positive equilibrium provided the net reproductive number is larger than one. If it is smaller than one, then the extinction equilibrium is globally asymptotically stable...

We study the problem of straight-line path following for fully actuated marine craft. We propose a controller that adjusts the speed of the marine craft according to the geometric distance and the rate of convergence to the path. The control law is derived using the method of least squares, which is used to find an approximate solution for overdetermined systems. The conditions under which the ...

This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov’s stability theo...

According to biological strategy for pest control, a mathematical model with periodic releasing virus particles for insect viruses attacking pests is considered. By using Floquet’s theorem, small-amplitude perturbation skills and comparison theorem, we prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically stable pesteradication period...

In this paper, a system of three globally coupled limit cycle oscillators with a linear time-delayed coupling are investigated. Considering the delay as a parameter, we also study the effect of time delay on the dynamics. Next, Hopf bifurcations induced by time delays using the normal form theory and center manifold reduction are obtained. Based on the symmetric Hopf bifurcation theorem, we inv...

We consider the time-dependent nonlinear system q̇(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uni...

The paper deals with the synthesis of a non-fragile state controller with reduced design complexity for a class of continuous-time nonlinear delayed symmetric composite systems. Additive controller gain perturbations are considered. Both subsystems and interconnections include time-delays. A low-order control design system is first constructed. Then, stabilizing controllers with norm bounded ga...

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

The verification of the self-stabilization property of a distributed algorithm is a complicated task. By exploiting certain analogies between self-stabilizing distributed algorithms and globally asymptotically stable feedback systems, techniques originally developed for the verification of feedback system stability can be adopted for the verification of selfstabilization of distributed algorith...