Statistical properties for a dissipative model of relativistic particles in a wave packet: A parameter space investigation

Author(s)

Hansen, Matheus ^[1] ; da Costa, Diogo R. ^{[2, 3, 1]} ; Oliveira, Diego F. M. ^{[1, 4]} ; Leonel, Edson D. ^{[1, 5]}

Affiliation

^[1] Univ Estadual Paulista, UNESP, Dept Fis, BR-13506900 Rio Claro, SP - Brazil

^[2] Univ Sao Paulo, Inst Fis, BR-05314970 Sao Paulo - Brazil

^[3] Univ Bristol, Sch Math, Bristol, Avon - England

^[4] Indiana Univ, Sch Informat & Comp, Ctr Complex Networks & Syst Res, Bloomington, IN 47408 - USA

^[5] Abdus Salam Int Ctr Theoret Phys, I-34151 Trieste - Italy

• Document type: Journal article
• Source: Applied Mathematics and Computation; v. 238, p. 387-392, JUL 1 2014.
• Web of Science Citations: 4

Abstract

Some statistical and dynamical properties for the problem of relativistic charged particles in a wave packet are studied. We show that the introduction of dissipation change the structure of the phase space and attractors appear. Additionally, by changing at least one of the control parameters, the unstable manifold touches the stable manifold of the same saddle fixed point and a boundary crisis occurs. We show that the chaotic attractor is destroyed given place to a transient which follows a power law with exponent -1 when varying the control parameters near the criticalities. On the other hand, by changing at least two control parameters and by using the Lyapunov exponents to classify orbits with chaotic and periodic behaviour, we show the existence of infinite shrimp-shaped domains, which correspond to the periodic attractors, embedded in a region with chaotic behaviour. Finally, we show the first indication of a shrimp in a three dimension parameter space. (C) 2014 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/01449-1 - Statistical and dynamical properties of time-dependent systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• 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: 12/18962-0 - Transport, escape of particles and dynamical properties of some non-linear mappings
• Grantee: Diogo Ricardo da Costa
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 13/22764-2 - Dynamical and transport properties in conservative and dissipative dynamical systems
• Grantee: Diogo Ricardo da Costa
• Support Opportunities: Scholarships in Brazil - Post-Doctoral