Implicit Mapping Dynamics

Abstract

This chapter presents a Yin–Yang theory for implicit, nonlinear, discrete dynamical systems with consideration of positive and negative iterations of discrete iterative maps. In existing analysis, the solutions relative to “Yang” in nonlinear dynamical systems are extensively investigated. However, the solutions pertaining to “Yin” in nonlinear dynamical systems are not investigated yet. A set of concepts on “Yin” and “Yang” in implicit, nonlinear, discrete dynamical systems are introduced. Based on the Yin–Yang theory, the complete dynamics of implicit discrete dynamical systems can be discussed. A discrete dynamical system with the Henon map is investigated as an example. Period-m solutions, stability, and bifurcations for multi-step, implicit discrete systems will be discussed.