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Nonlinear dynamics

Abstract

We apply basic theories of chaos and turbulence to investigate and control chaotic dynamical systems. For Hamiltonian systems, we investigate the transition to chaos and the onset and break of transport barriers, as observed in magnetically confined plasmas and particle accelerators. We also investigate the turbulence onset in magnetically confined plasmas and interpret control experiments in tokamaks and helimaks. Moreover, we also investigate chaotic dissipative systems, found in applied physics and engineering, and identify dynamical properties of these systems in the parameter space. We perform experiments on the Matsumoto-Chua circuit, faucet formation, bubble formation, and mechanical systems. (AU)

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Scientific publications (59)
(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)
PALMERO, MATHEUS S.; LIVORATI, ANDRE L. P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 65, p. 248-259, . (15/26699-6, 11/19296-1, 14/25316-3, 12/23688-5, 17/14414-2, 12/00556-6)
PROTACHEVICZ, P. R.; BORGES, R. R.; REIS, A. S.; BORGES, F. S.; IAROSZ, K. C.; CALDAS, I. L.; LAMEU, E. L.; MACAU, E. E. N.; VIANA, R. L.; SOKOLOV, I. M.; et al. Synchronous behaviour in network model based on human cortico-cortical connections. Physiological Measurement, v. 39, n. 7, . (15/50122-0, 16/23398-8, 11/19296-1, 17/20920-8, 15/07311-7, 17/13502-5, 17/18977-1)
FERRARI, F. A. S.; VIANA, R. L.; REIS, A. S.; IAROSZ, K. C.; CALDAS, I. L.; BATISTA, A. M.. A network of networks model to study phase synchronization using structural connection matrix of human brain. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 496, p. 162-170, . (15/07311-7, 11/19296-1, 17/20920-8)
FERRO, R. M.; CALDAS, I. L.. Internal transport barriers in plasmas with reversed plasma flow. Physics Letters A, v. 382, n. 15, p. 1014-1019, . (11/19296-1)
DEPETRI, GABRIELA I.; PEREIRA, FELIPE A. C.; MARIN, BORIS; BAPTISTA, MURILO S.; SARTORELLI, J. C.. Dynamics of a parametrically excited simple pendulum. Chaos, v. 28, n. 3, . (11/19296-1, 14/07043-0, 17/04748-0)
DE SOUSA, M. C.; CALDAS, I. L.. Improving particle beam acceleration in plasmas. Physics of Plasmas, v. 25, n. 4, . (15/05186-0, 11/19296-1)
PEREIRA, F. A. C.; HERNANDEZ, W. A.; TOUFEN, D. L.; GUIMARAES-FILHO, Z. O.; CALDAS, I. L.; GENTLE, K. W.. Burst temperature from conditional analysis in Texas Helimak and TCABR tokamak. Physics of Plasmas, v. 25, n. 4, . (11/19296-1, 14/07043-0, 15/50122-0)
HANSEN, MATHEUS; CIRO, DAVID; CALDAS, IBERE L.; LEONEL, EDSON D.. Explaining a changeover from normal to super diffusion in time-dependent billiards. EPL, v. 121, n. 6, . (17/14414-2, 11/19296-1)
MUGNAINE, MICHELE; REIS, ADRIANE S.; BORGES, FERNANDO S.; BORGES, RAFAEL R.; FERRARI, FABIANO A. S.; IAROSZ, KELLY C.; CALDAS, IBERE L.; LAMEU, EWANDSON L.; VIANA, RICARDO L.; SZEZECH, JR., JOSE D.; et al. Delayed feedback control of phase synchronisation in a neuronal network model. European Physical Journal-Special Topics, v. 227, n. 10-11, p. 1151-1160, . (17/18977-1, 17/20920-8, 11/19296-1, 15/07311-7, 16/23398-8, 17/13502-5, 15/50122-0)
LAMEU, E. L.; MACAU, E. E. N.; BORGES, F. S.; IAROSZ, K. C.; CALDAS, I. L.; BORGES, R. R.; PROTACHEVICZ, P. R.; VIANA, R. L.; BATISTA, A. M.. Alterations in brain connectivity due to plasticity and synaptic delay. European Physical Journal-Special Topics, v. 227, n. 5-6, p. 673-682, . (17/18977-1, 17/20920-8, 11/19296-1, 15/07311-7, 16/23398-8, 17/13502-5, 15/50122-0)
HERNANDEZ, W. A.; GUIMARAES-FILHO, Z.; GRENFELL, G. G.; NASCIMENTO, I. C.. Spatial inhomogeneity effects on burst temperature estimation using a triple probe configuration in Tokamak Chauffage Alfven Bresilien tokamak. JOURNAL OF PLASMA PHYSICS, v. 85, n. 4, . (18/03211-6, 11/19296-1)
BORGES, F. S.; PROTACHEVICZ, P. R.; PENA, R. F. O.; LAMEU, E. L.; HIGA, V, G. S.; KIHARA, J. A. H.; MATIAS, F. S.; ANTONOPOULOS, C. G.; DE PASQUALE, R.; ROQUE, A. C.; et al. Self-sustained activity of low firing rate in balanced networks. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 537, . (16/23398-8, 13/07699-0, 15/50122-0, 17/18977-1, 15/07311-7, 11/19296-1, 17/13502-5, 17/20920-8, 17/26439-0, 13/25667-8)
DE SOUSA, M. C.; MARCUS, F. A.; CALDAS, I. L.; VIANA, R. L.. Energy distribution in intrinsically coupled systems: The spring pendulum paradigm. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 509, p. 1110-1119, . (15/05186-0, 11/19296-1)
LAMEU, E. L.; YANCHUK, S.; MACAU, E. E. N.; BORGES, F. S.; IAROSZ, K. C.; CALDAS, I. L.; PROTACHEVICZ, P. R.; BORGES, R. R.; VIANA, R. L.; SZEZECH, JR., J. D.; et al. Recurrence quantification analysis for the identification of burst phase synchronisation. Chaos, v. 28, n. 8, . (17/18977-1, 17/20920-8, 11/19296-1, 15/07311-7, 16/23398-8, 17/13502-5, 15/50122-0)
SANTOS, V.; SZEZECH, JR., J. D.; BATISTA, A. M.; IAROSZ, K. C.; BAPTISTA, M. S.; REN, H. P.; GREBOGI, C.; VIANA, R. L.; CALDAS, I. L.; MAISTRENKO, Y. L.; et al. Riddling: Chimera's dilemma. Chaos, v. 28, n. 8, . (17/20920-8, 15/07311-7, 11/19296-1, 15/05186-0, 15/50122-0)
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, IBERE L.; FEUDEL, ULRIKE. Boundaries of synchronization in oscillator networks. Physical Review E, v. 98, n. 3, . (13/26598-0, 17/05521-0, 15/50122-0, 11/19296-1)
LAMEU, EWANDSON L.; BORGES, FERNANDO S.; LAROSZ, KELLY C.; PROTACHEVICZ, PAULO R.; ANTONOPOULOS, CHRIS G.; MACAU, ELBERT E. N.; BATISTA, ANTONIO M.. Short-term and spike-timing-dependent plasticity facilitate the formation of modular neural networks. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 96, . (15/50122-0, 17/13502-5, 16/23398-8, 15/07311-7, 17/18977-1, 17/20920-8, 20/04624-2, 11/19296-1)
PROTACHEVICZ, P. R.; BORGES, F. S.; IAROSZ, K. C.; CALDAS, I. L.; BAPTISTA, M. S.; VIANA, R. L.; LAMEU, E. L.; MACAU, E. E. N.; BATISTA, A. M.. How synapses can enhance sensibility of a neural network. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 492, p. 1045-1052, . (15/07311-7, 11/19296-1, 16/23398-8, 16/16148-5, 15/50122-0)
FRAILE, JR., ANDRE CARLOS; ROBERTO, MARISA; CALDAS, IBERE LUIZ; LOPES MARTINS, CAROLINE GAMEIRO. Plasma Response to Resonant Magnetic Perturbations in Large Aspect Ratio Tokamaks. IEEE TRANSACTIONS ON PLASMA SCIENCE, v. 45, n. 11, p. 2906-2912, . (15/16471-8, 11/19296-1)
VISCONDI, THIAGO F.; CALDAS, IBERE L.; MORRISON, PHILIP J.. A method for Hamiltonian truncation: a four-wave example. Journal of Physics A-Mathematical and Theoretical, v. 49, n. 16, . (12/20452-0, 11/19296-1)
OYARZABAL, R. S.; SZEZECH, JR., J. D.; BATISTA, A. M.; DE SOUZA, S. L. T.; CALDAS, I. L.; VIANA, R. L.; SANJUAN, M. A. F.. Transient chaotic transport in dissipative drift motion. Physics Letters A, v. 380, n. 18-19, p. 1621-1626, . (11/19296-1)
ABUD, C. V.; CALDAS, I. L.. On Slater's criterion for the breakup of invariant curves. PHYSICA D-NONLINEAR PHENOMENA, v. 308, p. 34-39, . (11/19296-1, 13/17989-5)
MEDEIROS, E. S.; CALDAS, I. L.; BAPTISTA, M. S.. Sensitive dependence on parameters of continuous-time nonlinear dynamical systems. CHAOS SOLITONS & FRACTALS, v. 99, p. 16-19, . (11/19296-1, 13/26598-0)
DA FONSECA, J. D.; DEL-CASTILLO-NEGRETE, D.; SOKOLOV, I. M.; CALDAS, I. L.. A statistical study of gyro-averaging effects in a reduced model of drift-wave transport. Physics of Plasmas, v. 23, n. 8, . (12/10240-6, 11/19296-1)
BORGES, R. R.; BORGES, F. S.; LAMEU, E. L.; BATISTA, A. M.; IAROSZ, K. C.; CALDAS, I. L.; ANTONOPOULOS, C. G.; BAPTISTA, M. S.. Spike timing-dependent plasticity induces non-trivial topology in the brain. NEURAL NETWORKS, v. 88, p. 58-64, . (15/07311-7, 16/16148-5, 11/19296-1)
LIVORATI, ANDRE L. P.; PALMERO, MATHEUS S.; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard. Journal of Physics A-Mathematical and Theoretical, v. 47, n. 36, . (12/00556-6, 11/19296-1, 12/23688-5)
LIVORATI, ANDRE L. P.; CALDAS, IBERE L.; DETTMANN, CARL P.; LEONEL, EDSON D.. Crises in a dissipative bouncing ball model. Physics Letters A, v. 379, n. 43-44, p. 2830-2838, . (11/19296-1, 14/25316-3, 12/23688-5)
DOS SANTOS, VAGNER; SZEZECH, JR., JOSE D.; BAPTISTA, MURILO S.; BATISTA, ANTONIO M.; CALDAS, IBERE L.. Unstable dimension variability structure in the parameter space of coupled Henon maps. Applied Mathematics and Computation, v. 286, p. 23-28, . (11/19296-1)
BARTOLONI, B.; SCHELIN, A. B.; CALDAS, I. L.. Shearless bifurcation on symplectic maps of magnetic field lines in tokamaks with reversed current. Physics Letters A, v. 380, n. 31-32, p. 2416-2421, . (12/18073-1, 11/19296-1)
DEPETRI, G. I.; SARTORELLI, J. C.; MARIN, B.; BAPTISTA, M. S.. Tilted excitation implies odd periodic resonances. Physical Review E, v. 94, n. 1, . (11/19296-1)
MAURO CATTANI; IBERÊ LUIZ CALDAS; SILVIO LUIZ DE SOUZA; KELLY CRISTIANE IAROSZ. Teoria do Caos Determinístico: Conceitos Básicos. Revista Brasileira de Ensino de Física, v. 39, n. 1, . (11/19296-1, 15/07311-7)
ROSALEM, K. C.; ROBERTO, M.; CALDAS, I. L.. Drift-wave transport in the velocity shear layer. Physics of Plasmas, v. 23, n. 7, . (15/16471-8, 11/19296-1)
MARCUS, F. A.; ROBERTO, M.; CALDAS, I. L.; ROSALEM, K. C.; ELSKENS, Y.. Influence of the radial electric field on the shearless transport barriers in tokamaks. Physics of Plasmas, v. 26, n. 2, . (15/16471-8, 11/19296-1)
SANTOS, MOISES S.; SZEZECH, JR., JOSE D.; BATISTA, ANTONIO M.; IAROSZ, KELLY C.; CALDAS, IBERE L.; VIANA, RICARDO L.. Dragon-kings death in nonlinear wave interactions. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 534, . (15/07311-7, 11/19296-1, 15/50122-0)
CIRO, DAVID; CALDAS, IBERE L.; VIANA, RICARDO L.; EVANS, TODD E.. Efficient manifolds tracing for planar maps. Chaos, v. 28, n. 9, . (11/19296-1, 12/18073-1)
BORGES, R. R.; BORGES, F. S.; LAMEU, E. L.; BATISTA, A. M.; IAROSZ, K. C.; CALDAS, I. L.; VIANA, R. L.; SANJUAN, M. A. F.. Effects of the spike timing-dependent plasticity on the synchronisation in a random Hodgkin-Huxley neuronal network. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 34, p. 12-22, . (15/07311-7, 11/19296-1)
VISCONDI, THIAGO F.; CALDAS, IBERE L.; MORRISON, PHILIP J.. Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories. Physics of Plasmas, v. 24, n. 3, . (12/20452-0, 11/19296-1)
LAMEU, EWANDSON L.; BORGES, FERNANDO S.; BORGES, RAFAEL R.; IAROSZ, KELLY C.; CALDAS, IBERE L.; BATISTA, ANTONIO M.; VIANA, RICARDO L.; KURTHS, JUERGEN. Suppression of phase synchronisation in network based on cat's brain. Chaos, v. 26, n. 4, . (11/50151-0, 15/07311-7, 11/19296-1)
TOUFEN, D. L.; PEREIRA, F. A. C.; GUIMARAES-FILHO, Z. O.; CALDAS, I. L.; GENTLE, K. W.. Electrostatic turbulence intermittence driven by biasing in Texas Helimak. Physics of Plasmas, v. 21, n. 12, . (12/22108-5, 11/19296-1)
LIVORATI, ANDRE L. P.; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. On the statistical and transport properties of a non-dissipative Fermi-Ulam model. Chaos, v. 25, n. 10, . (11/19296-1, 14/25316-3, 12/23688-5)
DE SOUSA, M. C.; CALDAS, I. L.; OZORIO DE ALMEIDA, A. M.; RIZZATO, F. B.; PAKTER, R.. Alternate islands of multiple isochronous chains in wave-particle interactions. Physical Review E, v. 88, n. 6, . (11/20794-6, 11/19296-1)
ROSALEM, K. C.; ROBERTO, M.; CALDAS, I. L.. Influence of the electric and magnetic shears on tokamak transport. NUCLEAR FUSION, v. 54, n. 6, . (13/03401-6, 11/19296-1)
CIRO, D.; CALDAS, I. L.. Magnetic topology and current channels in plasmas with toroidal current density inversions. Physics of Plasmas, v. 20, n. 10, . (12/18073-1, 11/19296-1)
KROETZ, TIAGO; LIVORATI, ANDRE L. P.; LEONEL, EDSON D.; CALDAS, IBERE L.. Global ballistic acceleration in a bouncing-ball model. Physical Review E, v. 92, n. 1, . (11/19296-1, 14/25316-3, 12/23688-5)
ABUD, C. V.; CALDAS, I. L.. Impact of punctual flat magnetic shear on the field line transport. Physics of Plasmas, v. 22, n. 6, . (11/19296-1, 13/17989-5)
BORGES, F. S.; PROTACHEVICZ, P. R.; LAMEU, E. L.; BONETTI, R. C.; IAROSZ, K. C.; CALDAS, I. L.; BAPTISTA, M. S.; BATISTA, A. M.. Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model. NEURAL NETWORKS, v. 90, p. 1-7, . (16/16148-5, 15/07311-7, 11/19296-1)
SANTOS, M. S.; SZEZECH, J. D.; BORGES, F. S.; IAROSZ, K. C.; CALDAS, I. L.; BATISTA, A. M.; VIANA, R. L.; KURTHS, J.. Chimera-like states in a neuronal network model of the cat brain. CHAOS SOLITONS & FRACTALS, v. 101, p. 86-91, . (11/50151-0, 15/07311-7, 16/16148-5, 11/19296-1)
BORGES, F. S.; LAMEU, E. L.; IAROSZ, K. C.; PROTACHEVICZ, P. R.; CALDAS, I. L.; VIANA, R. L.; MACAU, E. E. N.; BATISTA, A. M.; BAPTISTA, M. S.. Inference of topology and the nature of synapses, and the flow of information in neuronal networks. Physical Review E, v. 97, n. 2, . (16/16148-5, 15/50122-0, 11/19296-1, 15/07311-7, 16/23398-8)
SANTOS, M. S.; SZEZECH, JR., J. D.; BATISTA, A. M.; CALDAS, I. L.; VIANA, R. L.; LOPES, S. R.. Recurrence quantification analysis of chimera states. Physics Letters A, v. 379, n. 37, p. 2188-2192, . (11/19296-1)
CALDAS, IBERE LUIZ; BARTOLONI, BRUNO F.; CIRO, DAVID; ROBERSON, GERALDO; SCHELIN, ADRIANE B.; KROETZ, TIAGO; ROBERTO, MARISA; VIANA, RICARDO LUIZ; IAROSZ, KELLY CRISTIANE; BATISTA, ANTONIO MARCOS; et al. Symplectic Maps for Diverted Plasmas. IEEE TRANSACTIONS ON PLASMA SCIENCE, v. 46, n. 7, 1, SI, p. 2354-2361, . (15/07311-7, 11/19296-1, 12/18073-1)
BORGES, RAFAEL R.; BORGES, FERNANDO S.; LAMEU, EWANDSON L.; PROTACHEVICZ, PAULO R.; IAROSZ, KELLY C.; CALDAS, IBERE L.; VIANA, RICARDO L.; MACAU, ELBERT E. N.; BAPTISTA, MURILO S.; GREBOGI, CELSO; et al. Synaptic Plasticity and Spike Synchronisation in Neuronal Networks. Brazilian Journal of Physics, v. 47, n. 6, p. 678-688, . (16/16148-5, 15/50122-0, 11/19296-1, 15/07311-7, 16/23398-8)
MATHIAS, A. C.; KROETZ, T.; CALDAS, I. L.; VIANA, R. L.. Chaotic magnetic field lines and fractal structures in a tokamak with magnetic limiter. CHAOS SOLITONS & FRACTALS, v. 104, p. 588-598, . (11/19296-1)
EVARISTO, RONALDO M.; BATISTA, ANTONIO M.; VIANA, RICARDO L.; IAROSZ, KELLY C.; SZEZECH, JR., JOSE D.; DE GODOY, MOACIR F.. Mathematical model with autoregressive process for electrocardiogram signals. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 57, p. 415-421, . (16/16148-5, 15/07311-7, 11/19296-1)
PEREIRA, F. A. C.; TOUFEN, D. L.; GUIMARAES-FILHO, Z. O.; CALDAS, I. L.; GENTLE, K. W.. Burst propagation in Texas Helimak. Plasma Physics and Controlled Fusion, v. 58, n. 5, SI, . (12/22108-5, 11/19296-1, 14/07043-0)
FRAILE JUNIOR, ANDRE CARLOS; ROBERTO, MARISA; CALDAS, IBERE LUIZ. Plasma Response to Resonant Perturbations at Tokamak Edge. Brazilian Journal of Physics, v. 48, n. 4, p. 426-432, . (15/16471-8, 11/19296-1)
MEDEIROS, EVERTON S.; CALDAS, IBERE L.; BAPTISTA, MURILO S.; FEUDEL, ULRIKE. Trapping Phenomenon Attenuates the Consequences of Tipping Points for Limit Cycles. SCIENTIFIC REPORTS, v. 7, . (13/26598-0, 11/19296-1, 15/20407-3)
ROBERSON, GERALDO; ROBERTO, MARISA; CALDAS, IBERE LUIZ; KROETZ, TIAGO; VIANA, RICARDO LUIZ. Shaping Diverted Plasmas With Symplectic Maps. IEEE TRANSACTIONS ON PLASMA SCIENCE, v. 45, n. 3, p. 356-363, . (15/16471-8, 11/19296-1)
NOGUEIRA, T. N.; PEREIRA, F. A. C.; PROCOPIO, J.; SARTORELLI, J. C.. Dripping faucet dynamics in a nonuniform electric field. Chaos, v. 28, n. 11, . (11/19296-1, 14/07043-0)
HANSEN, MATHEUS; DA COSTA, DIOGO RICARDO; CALDAS, IBERE L.; LEONEL, EDSON D.. Statistical properties for an open oval billiard: An investigation of the escaping basins. CHAOS SOLITONS & FRACTALS, v. 106, p. 355-362, . (13/22764-2, 11/19296-1, 12/23688-5, 17/14414-2, 14/00334-9)

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