Boundary crises and supertrack orbits in the Gauss map

Author(s)

de Oliveira, Juliano A. ; de Mendonca, Hans M. J. ; Favarim, Vitor A. ; de Carvalho, R. Egydio ; Leonel, Edson D.

• Document type: Journal article
• Source: European Physical Journal-Special Topics; v. 231, n. 3, p. 4-pg., 2022-01-25.

Abstract

Supertrack orbits are used to investigate boundary crises in an one-dimensional, two-parameter (v, beta), nonlinear Gauss map. After the crises, the time evolution of the orbit is shown to be pseudo-chaotic. We investigate the chaotic transient, that is, the time an orbit spends in a region where the chaotic attractor existed prior to the crisis, and confirm it decays exponentially with time. The relaxation time is given by a power-law tau proportional to mu(gamma) with mu = vertical bar beta - beta(c)vertical bar corresponding to the distance measured in the parameter where the crises are observed. beta(c )is the parameter that characterizes the occurrence of a boundary crisis and the numerical value of the power measured was gamma = 1/2. (AU)

• FAPESP's process: 21/09519-5 - Characterization of phase transitions in nonlinear systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/23688-5 - Exponents and scaling laws, phase transitions and transport properties of time dependent systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/07329-4 - Analysis of the robustness of the shearless attractor (curve) and the quasi-periodic chaotic transition
• Grantee: Ricardo Egydio de Carvalho
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/14685-9 - Transport properties and bifurcation analysis in nonlinear dynamical systems
• Grantee: Juliano Antonio de Oliveira
• Support Opportunities: Regular Research Grants
• FAPESP's process: 15/22062-3 - Scaling properties and cascades bifurcations in one-dimensional discrete maps
• Grantee: Hans Muller Junho de Mendonça
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 19/14038-6 - Investigation of dynamical properties in nonlinear systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants