The dynamical analysis of a new chaotic system and simulation

Abstract

In this paper, we make a study of dynamical properties of a nonlinear monetary system (1.1) towards the solution of the localization problem of compact invariant sets of the system (1.1). Here, a localization signifies a description of a set containing all compact invariant sets of (1.1) in terms of equalities and inequalities defined in the state space R3. Our approach is based on using the first-order extremum conditions and is realized with the help of the iterative theory. We claim that all compact invariant sets of this system are located in the intersection of a ball with two frusta, and we also compute its corresponding parameters of the system. In addition, localization with the help of a two-parameter set of parabolic cylinders is described. Numerical simulation is consistent with the results of theoretical calculation. Copyright © 2013 John Wiley & Sons, Ltd.