ABSTRACT

A new class of phenomena has recently been discovered three centuries after the publication of Newton’s Principia in nonlinear dynamics. The theory of nonlinear dynamics is strongly associated with the bifurcation theory. Modifying the parameters of a nonlinear system, the location and the number of equilibrium points can change. The nonlinear dynamical systems have two broad classes: autonomous systems and non-autonomous systems. Both are described by a set of first-order nonlinear differential equations and can be represented in state space. The nonlinear world is much more colorful than the linear one. The nonlinear systems can be in various states, one of them is the equilibrium point. Two- or higher-dimensional nonlinear systems can exhibit periodic motion without external periodical excitation. To obtain complete understanding of the global dynamics of nonlinear systems, the knowledge of invariant manifolds is absolutely crucial. The invariant manifolds or briefly the manifolds are borders in state space separating regions.