Abstract: Dynamical systems governed by discrete time-difference equations are referred to as point mapping dynamical systems in this paper. Based upon the Poincaré theory of index for vector fields, a ...

Abstract: The method of point-to-point mappings has been receiving increasing attention in recent years. In this paper we discuss instead dynamical systems governed by cell-to-cell mappings. The justifications ...

Abstract: A dynamical system having multiple degrees of freedom and under parametric excitation is governed by a system of ordinary differential equations with periodic coefficients. In this paper a ...

Abstract: This paper is concerned with the generalization of Poincaré’s theory of index to systems of order higher than two. The basic tool used in the generalization is the concept of the degree of ...

Abstract: The simple theory of cell mapping and the associated algorithm presented in [1, 2] have been found to form a very effective tool for the global analysis of nonlinear systems. In this paper ...

Abstract: Given in this paper is the development of a theory for dynamical systems subjected to periodic impulsive parametric excitations. By periodic impulsive parametric excitation we mean those excitations ...

Abstract: The dynamic stability of simply supported, shallow arches subjected to timewise step loads is studied in this paper. Presented is a general method which allows us to treat arches of arbitrary ...

Abstract: A second-order nonlinear system subjected to parametric excitation is investigated. The nonlinear factors included are nonlinear damping and a cubic term in displacement. The primary purpose of ...

Abstract: A class of systems of coupled Hill’s equations is studied. It is shown that for systems of equations in this class, completely decoupled Hill’s equations may be obtained and the stability of ...