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...

This paper presents results for stability and robustness of hybrid systems consisting of nonlinear subsystems. Present stability results that are extensions of classical Lyapunov theory are restricted to certain kinds of hybrid systems. For example, it is required that all subsystems have the same equilibrium point. In this paper, existing results are generalized; but more importantly, it is sh...

The paper is a non-technical survey and is aimed to illustrate Dolgopyat’s profound contributions to smooth ergodic theory. I will discuss some of Dolgopyat’s work on partial hyperbolicity and nonuniform hyperbolicity with emphasis on interaction between the two – the class of dynamical systems with mixed hyperbolicity. On the one hand, this includes uniformly partially hyperbolic diffeomorphis...

We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of Pk and prove that it is equivalent to the stability of repelling cycles or the existence of a measurable holomorphic motion of Julia sets. We characterize the corresponding bifurcations by the strict subharmonicity of the sum of Lyapunov exponents or the instability of critical dynamics and a...

In this paper, Lyapunov Theory is combining with fuzzy merging algorithm to solve the non-linear solutions. The non-linear points are found using fuzzy c-means merging by reciprocating the distance. The Gaussian weights are used in combining the fuzzy merging with Lyapunov Theory. A vector equals the centers of two points; the weights are concentrated mostly on widely distributed region than th...

−− This paper proposes a robustness analysis for a dissolved oxygen controller based on Lyapunov theory. The control strategy is designed for the Bacillus thuringiensis δ-endotoxins production process. First, the control strategy is presented and second, it is considered with a biomass estimator in closed loop and it is shown a robustness analysis for the errors introduced by both: biomass esti...