In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey model in the closed first quadrant [Formula: see text]. The existence and local stability of the unique positive equilibrium of the model are analyzed algebraically. It is shown that the model can undergo a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium an...

This paper presents a new model-based adaptive controller and proof of its global asymptotic stability with respect to the standard rigid-body model of robot-arm dynamics. Experimental data from a study of one new and several established globally asymptotically stable adaptive controllers on two very different robot arms 1) demonstrate the superior tracking performance afforded by the model-bas...

Abstract. In this paper, we study a class of multi-group SIRS epidemic models with nonlinear incidence rate which have cross patch infection between different groups. The basic reproduction number R0 is calculated. By using the method of Lyapunov functions, LaSalle’s invariance principle, the theory of the nonnegative matrices and the theory of the persistence of dynamical systems, it is proved...

In this paper, some properties of all positive solutions are considered for a higher order rational difference equation, mainly for the existence of eventual prime period two solutions, the existence and asymptotic behavior of nonoscillatory solutions and the global asymptotic stability of its equilibria. Our results show that a positive equilibrium point of this equation is a global attractor ...

Criteria for global asymptotic stability of a null solution of a nonlinear differential equation of fifth order with delay x(t) + ψ(x(t− r), x′(t− r), x′′(t− r), x′′′(t− r), x(t− r))x(t) +f(x′′(t− r), x′′′(t− r)) + α3x(t) + α4x(t) + α5x(t) = 0 are obtained by using Lyapunov’s second method. By defining a Lyapunov functional, sufficient conditions are established, which guarantee the null soluti...

We present arguments for the existence of both globally regular and black hole solutions of the Einstein equations with a conformally coupled scalar field, in the presence of a negative cosmological constant, for space-time dimensions greater than or equal to four. These configurations approach asymptotically anti-de Sitter spacetime and are indexed by the central value of the scalar field. We ...

An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to an...

The dynamical equations for a spinning top are derived in which the orientation is speciied by a complex variable using stereographic projection of Poisson's equations. Necessary and suucient conditions for Lyapunov stability of the uncontrolled motion of the spinning top are derived using the Energy-Casimir method. Control laws that globally asymptotically stabilize the spinning top to the sle...

We derive stability conditions for Model Predictive Control (MPC) with hard constraints on the inputs and \soft" constraints on the outputs for an innnitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly i...

Given a vector eld X on the real plane, we study the innuence of the curvature of the orbits of _ x = X ? (x) in the stability of those of the system _ x = X(x). We pay special attention to the case in which this curvature is negative in the whole plane. Under this assumption, we classify the possible critical points and give a criterion for a point to be globally asymptotically stable. In the ...