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Investigation of dynamical properties in nonlinear systems

Grant number: 19/14038-6
Support Opportunities:Regular Research Grants
Duration: December 01, 2019 - November 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Physics - General Physics
Principal Investigator:Edson Denis Leonel
Grantee:Edson Denis Leonel
Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The subject of investigation of this project is the study of the several dynamical properties present in nonlinear systems. In dynamical systems described either by differential equations or discrete mappings, quite often we find observables that are described by a power law. Examples include Lyapunov exponents, diffusion coefficient, quadratic mean velocity, periodic structures in the parameter plane producing objects called as shrimps, distance from the attractor, chaotic transient, the attractor itself either periodic or chaotic, among many others. When such measurable quantities are also scaling invariant, generally made via a control parameter or change in the initial condition, one can find a set of critical exponents that describe the dynamics of the observable by using scaling transformations. The main phenomenology to describe this property uses a set of scaling hypotheses as well as a generalized homogeneous function. From them, it is possible to find an analytic relation for the exponents leading to a scaling law. Indeed, scaling laws are much useful in the characterization and definition of classes of universality and can be proved either using numerical simulations or analytic descriptions. When the characterization is not given in terms of power, as it is the case of the anomalous diffusion in chaotic systems, often the properties are characterized by other laws including exponentials, stretched exponential among many others. Following this thematic, the most distinct dynamical properties in several nonlinear dynamical systems either described by ordinary differential equations or by mappings, will be investigated. Some of them include the characterization of chaotic seas, chaotic transport, the transition from integrability to no integrability, time-dependent billiards among others. (AU)

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Scientific publications (20)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
HANSEN, MATHEUS; LANES, GABRIEL C.; BRITO, VINICIUS L. G.; LEONEL, EDSON D.. Investigation of pollen release by poricidal anthers using mathematical billiards. Physical Review E, v. 104, n. 3, . (19/14038-6, 19/09150-1)
LEONEL, EDSON D.; KUWANA, CELIA MAYUMI; YOSHIDA, MAKOTO; DE OLIVEIRA, JULIANO ANTONIO. Chaotic diffusion for particles moving in a time dependent potential well. Physics Letters A, v. 384, n. 28, . (19/14038-6, 18/14685-9)
DA COSTA, DIOGO RICARDO; HANSEN, MATHEUS; SILVA, MARIO ROBERTO; LEONEL, EDSON D.. Tangent Method and Some Dynamical Properties of an Oval-Like Billiard. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 32, n. 04, p. 15-pg., . (19/14038-6, 20/02415-7, 19/09150-1)
GRACIANO, FLAVIO HELENO; DA COSTA, DIOGO RICARDO; LEONEL, EDSON D.; DE OLIVEIRA, JULIANO A.. Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well. Entropy, v. 24, n. 10, p. 15-pg., . (17/14414-2, 21/09519-5, 19/14038-6, 20/02415-7, 12/23688-5, 18/14685-9)
DE OLIVEIRA, JULIANO A.; DE MENDONCA, HANS M. J.; FAVARIM, VITOR A.; DE CARVALHO, R. EGYDIO; LEONEL, EDSON D.. Boundary crises and supertrack orbits in the Gauss map. European Physical Journal-Special Topics, v. 231, n. 3, p. 4-pg., . (21/09519-5, 12/23688-5, 19/07329-4, 18/14685-9, 15/22062-3, 19/14038-6)
DA FONSECA, JULIO D.; LEONEL, EDSON D.; MEDRANO-T, RENE O.. Density of instantaneous frequencies in the Kuramoto-Sakaguchi model. CHAOS SOLITONS & FRACTALS, v. 172, p. 12-pg., . (19/12930-9, 19/14038-6)
MIRANDA, LUCAS KENJI ARIMA; MORATTA, RAPHAEL; KUWANA, CELIA MAYUMI; YOSHIDA, MAKOTO; DE OLIVEIRA, JULIANO ANTONIO; LEONEL, EDSON DENIS. A second order phase transition characterized in the suppression of unlimited chaotic diffusion for a dissipative standard mapping. CHAOS SOLITONS & FRACTALS, v. 165, p. 4-pg., . (20/10602-1, 18/14685-9, 21/09519-5, 19/14038-6)
LEONEL, EDSON D.; MAYUMI KUWANA, CELIA; YOSHIDA, MAKOTO; ANTONIO DE OLIVEIRA, JULIANO. Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion. EPL, v. 131, n. 1, p. 5-pg., . (19/14038-6, 18/14685-9)
SILVEIRA, FELIPE AUGUSTO O.; ALVES, SIDINEY G.; LEONEL, EDSON D.; LADEIRA, DENIS G.. Dynamical aspects of a bouncing ball in a nonhomogeneous field. Physical Review E, v. 103, n. 6, . (19/14038-6)
DA SILVA, V. B.; VIEIRA, J. P.; LEONEL, EDSON D.. Fisher information of the Kuramoto model: A geometric reading on synchronization. PHYSICA D-NONLINEAR PHENOMENA, v. 423, . (19/14038-6)
DA FONSECA, JULIO D.; LEONEL, EDSON D.; CHATE, HUGUES. Instantaneous frequencies in the Kuramoto model. Physical Review E, v. 102, n. 5, . (19/14038-6, 19/12930-9)
LEONEL, EDSON D.; YOSHIDA, MAKOTO; DE OLIVEIRA, JULIANO ANTONIO. Characterization of a continuous phase transition in a chaotic system. EPL, v. 131, n. 2, . (19/14038-6, 18/14685-9)
DE OLIVEIRA, JULIANO A.; PERRE, RODRIGO M.; MENDEZ-BERMUDEZ, J. A.; LEONEL, EDSON D.. Leaking of orbits from the phase space of the dissipative discontinuous standard mapping. Physical Review E, v. 103, n. 1, . (18/14685-9, 19/06931-2, 19/14038-6)
MIRANDA, LUCAS K. A.; KUWANA, CELIA M.; HUGGLER, YONA H.; DA FONSECA, ANNE K. P.; YOSHIDA, MAKOTO; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. A short review of phase transition in a chaotic system. European Physical Journal-Special Topics, . (20/10602-1, 18/14685-9, 19/14038-6, 20/07219-1)
VELOSO HERMES, JOELSON D.; LEONEL, EDSON D.. Characteristic Times for the Fermi-Ulam Model. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 31, n. 2, . (19/14038-6)
RANDO, DANILO S.; MARTI, ARTURO C.; LEONEL, EDSON D.. Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model. Chaos, v. 33, n. 2, p. 7-pg., . (19/14038-6)
MENDEZ-BERMUDEZ, J. A.; PERALTA-MARTINEZ, KEVIN; SIGARRETA, JOSE M.; LEONEL, EDSON D.. Leaking from the phase space of the Riemann-Liouville fractional standard map. CHAOS SOLITONS & FRACTALS, v. 172, p. 7-pg., . (19/14038-6)
DA SILVA, V. B.; VIEIRA, J. P.; LEONEL, EDSON D.. Information geometry theory of bifurcations? A covariant formulation. Chaos, v. 32, n. 2, p. 18-pg., . (19/14038-6)
DA FONSECA, JULIO D.; LEONEL, EDSON D.; CHATE, HUGUES. Instantaneous frequencies in the Kuramoto model. PHYSICAL REVIEW E, v. 102, n. 5, p. 18-pg., . (19/12930-9, 19/14038-6)
DE OLIVEIRA, JULIANO A.; PERRE, RODRIGO M.; MENDEZ-BERMUDEZ, J. A.; LEONEL, EDSON D.. Leaking of orbits from the phase space of the dissipative discontinuous standard mapping. PHYSICAL REVIEW E, v. 103, n. 1, p. 6-pg., . (19/14038-6, 18/14685-9, 19/06931-2)

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