Two-dimensional nonlinear map characterized by tunable Levy flights

Author(s)

Mendez-Bermudez, J. A. ; de Oliveira, Juliano A. ; Leonel, Edson D.

• Document type: Journal article
• Source: Physical Review E; v. 90, n. 4, p. 5-pg., 2014-10-27.

Abstract

After recognizing that point particles moving inside the extended version of the rippled billiard perform Levy flights characterized by a Levy-type distribution P(l) similar to l(-(1+alpha)) with alpha = 1, we derive a generalized two-dimensional nonlinear map M alpha able to produce Levy flights described by P(l) with 0 < alpha < 2. Due to this property, we call M alpha the Levy map. Then, by applying Chirikov's overlapping resonance criteria, we are able to identify the onset of global chaos as a function of the parameters of the map. With this, we state the conditions under which the Levy map could be used as a Levy pseudorandom number generator and furthermore confirm its applicability by computing scattering properties of disordered wires. (AU)

• 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: 13/14655-9 - Dynamical and statistical properties of nonlinear discontinuous maps
• Grantee: Edson Denis Leonel
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 14/18672-8 - Effects of dissipation, transient and dynamical properties in discrete mappings
• Grantee: Juliano Antonio de Oliveira
• Support Opportunities: Regular Research Grants