Dynamics of Multimodal Families of m-Modal Maps. (25th April 2022)

• Record Type: Journal Article
• Authors: González-Salas, S.; Cassal-Quiroga, B. B.; Tuxpan, J.; Campos, E.
• Other Names: Gambuzza Lucia Valentina Academic Editor.
• Is Part Of: Complexity. Volume 2022(2022)
• Publication Date: 2022-04-25
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2022/4340794
• Languages: English
• ISSNs: 1076-2787

Abstract

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 ⊂ ℝ, which is partitioned into non-uniform subdomains, with m ∈ 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.