Dynamics of Multimodal Families of m-Modal Maps

Abstract

In this work, we introduce families of multimodal maps based on logistic map, i.e., families of m-modal maps are defined on an interval $I\subset ℝ$ , which is partitioned into non-uniform subdomains, with $m\in \mathbb{N}$ . Because the subdomains of the partition are not uniform, each subdomain contains a unimodal map, given by the logistic map, that can have different heights. Therefore, we give the necessary and sufficient conditions for these modal maps present a multimodal family of m-modal maps, i.e., a bifurcation parameter can set a unimodal map, a bimodal map, up to a $m$ -modal map. Some numerical examples are given according to the developed theory. Some numerical examples are given in accordance with the developed theory.