The dynamics of a prey-predator system, where predator has two stages, a juvenile stage and a mature stage, is modelled by a system of three ordinary differential equations. Stability and permanence of the system are discussed. Furthermore, we consider the harvesting of prey species and obtain the maximum sustainable yield and the optimal harvesting policy.
The following time delay system is considered, where may have discontinuities, in particular at the origin. The solution is defined using the “redefined nonlinearity” concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given.
We study stability and stabilizability properties of systems with discontinuous righthand side (with solutions intended in Filippov's sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine with respect to the input: we give some sufficient conditions for a system to be stabilized by means of a feedback law of the Jurdjevic-Quinn...
In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.
This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear...
The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.