Work

Finding critical exponents and parameter space for a family of dissipative two-dimensional mappings

Year: 2024

Type: article

Abstract: A family of dissipative two-dimensional nonlinear mappings is considered. The mapping is described by the angle and action variables and parameterized by ε controlling nonlinearity, δ controlling the amount of dissipation, and an exponent γ is a dynamic free parameter that enables a connection with various distinct dynamic systems. The Lyapunov exponents are obtained for different values of the control parameters to characterize the chaotic attractors. We investigated the time evolution for the stationary state at period-doubling bifurcations. The convergence to the stationary state is made using a robust homogeneous and generalized function at the bifurcation parameter, which leads us to obtain a set of universal critical exponents. The parameter space of the mapping is investigated, and tangent, period-doubling, pitchfork, and cusp bifurcations are found, and a street of saddle-area and spring-area structures is observed.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0234491

Authors: Fábio H. da Costa, Mayla A. M. de Almeida, Rene O. Medrano-T, Edson D. Leonel, Juliano A. de Oliveira

Institutions: Universidade Estadual Paulista (Unesp), Instituto de Ciências Ambientais, Químicas e Farmacêuticas, Universidade Federal de São Paulo

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Financiadora de Estudos e Projetos