Existence and stability of solutions to nonlinear dynamical systems

This book is an outgrowth of our results on the existence and stability of solutions to nonlinear dynamical systems, stochastic systems, and impulsive systems over the last five years. In particular, we present the Razumikhin-type exponential stability criteria for impulsive stochastic functional differential systems, the stability analysis of neutral stochastic delay differential equations by a generalization of Banachs contraction principle and the globally asymptotical stability in the mean square for stochastic neural networks with time-varying delays and fixed moments of impulsive effect. Also, we discuss oscillation criteria based on a new weighted function for linear matrix Hamiltonian systems and the existences of the positive solutions or nontrivial solutions of nonlinear differential equations.

Autorentext

Yingxin Guo was born in Shandong, China, in 1969. He receivedthe B.Sc. degree in 2004, and the Ph.D. degree in 2012, respectively. He is currently a Lecture at Qufu Normal University. He is the author of more than 20 journal papers.His research interests include impulsive control, stochastic systems and time delay systems.