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Non linear dynamics

Abstract

We apply basic theories of chaos and turbulence to investigate the control of 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, mechanical systems (parametric pendula), and plasma turbulence and MHD instabilities in tokamaks. We also investigate the synchronization in neural networks, and the occurrence of chimeras and plasticity in these systems, and the syncrhronization of a network of non linear oscillators. (AU)

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Scientific publications (45)
(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)
TROBIA, JOSE; TIAN, KUN; BATISTA, ANTONIO M.; GREBOGI, CELSO; REN, HAI-PENG; SANTOS, MOISES S.; PROTACHEVICZ, PAULO R.; BORGES, FERNANDO S.; SZEZECH, JR., JOSE D.; VIANA, RICARDO L.; CALDAS, IBERE L.; IAROSZ, KELLY C. Mathematical model of brain tumour growth with drug resistance. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 103, DEC 2021. Web of Science Citations: 0.
LACERDA, JULIANA C.; FREITAS, CELSO; MACAU, ELBERT E. N.; KURTHS, JUERGEN. How heterogeneity in connections and cycles matter for synchronization of complex networks. Chaos, v. 31, n. 11 NOV 2021. Web of Science Citations: 0.
FREITAS, VANDER L. S.; YANCHUK, SERHIY; GRANDE, HELDER L. C.; MACAU, ELBERT E. N. The effects of time-delay and phase lags on symmetric circular formations of mobile agents. European Physical Journal-Special Topics, v. 230, n. 14-15, p. 2857-2864, OCT 2021. Web of Science Citations: 1.
PALMERO, MATHEUS S.; DIAZ, I, GABRIEL; CALDAS, IBERE L.; SOKOLOV, IGOR M. Sub-diffusive behavior in the Standard Map. European Physical Journal-Special Topics, v. 230, n. 14-15, p. 2765-2773, OCT 2021. Web of Science Citations: 1.
PRADO, THIAGO DE LIMA; MACAU, ELBERT EINSTEIN NEHRER; LOPES, SERGIO ROBERTO. Detection of data corruption in stationary time series using recurrence microstates probabilities. European Physical Journal-Special Topics, v. 230, n. 14-15, p. 2737-2744, OCT 2021. Web of Science Citations: 1.
DE LIMA, D. R.; CALDAS, I. L. Growth and performance of the periodic orbits of a nonlinear driven oscillator. CHAOS SOLITONS & FRACTALS, v. 150, SEP 2021. Web of Science Citations: 0.
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, IBERE L.; FEUDEL, ULRIKE. The impact of chaotic saddles on the synchronization of complex networks of discrete-time units. JOURNAL OF PHYSICS-COMPLEXITY, v. 2, n. 3 SEP 2021. Web of Science Citations: 0.
GOMES, J. V.; DE SOUSA, M. C.; VIANA, R. L.; CALDAS, I. L.; ELSKENS, Y. Low-dimensional chaos in the single wave model for self-consistent wave-particle Hamiltonian. Chaos, v. 31, n. 8 AUG 2021. Web of Science Citations: 0.
LACERDA, JULIANA C.; DIAS, JUSSARA; FREITAS, CELSO; MACAU, ELBERT. Vulnerability and stability of power grids modeled by second-order Kuramoto model: a mini review. European Physical Journal-Special Topics, AUG 2021. Web of Science Citations: 0.
OSORIO, L. A.; ROBERTO, M.; CALDAS, I. L.; VIANA, R. L.; ELSKENS, Y. Onset of internal transport barriers in tokamaks. Physics of Plasmas, v. 28, n. 8 AUG 2021. Web of Science Citations: 0.
REIS, ADRIANE S.; BRUGNAGO, EDUARDO L.; CALDAS, IBERE L.; BATISTA, ANTONIO M.; IAROSZ, KELLY C.; FERRARI, FABIANO A. S.; VIANA, RICARDO L. Suppression of chaotic bursting synchronization in clustered scale-free networks by an external feedback signal. Chaos, v. 31, n. 8 AUG 2021. Web of Science Citations: 0.
SILVEIRA, FRANCISCO E. M.; BENETTI, MONA HEGEL; CALDAS, IBERE LUIZ. Equation of State of the Kappa-Distributed Solar Wind Particles in the Earth's Magnetopause. SOLAR PHYSICS, v. 296, n. 7 JUL 2021. Web of Science Citations: 0.
FREITAS, VANDER L. S.; YANCHUK, SERHIY; GRANDE, HELDER L. C.; MACAU, ELBERT E. N. The effects of time-delay and phase lags on symmetric circular formations of mobile agents. European Physical Journal-Special Topics, JUN 2021. Web of Science Citations: 0.
PALMERO, MATHEUS S.; DIAZ, I, GABRIEL; CALDAS, IBERE L.; SOKOLOV, IGOR M. Sub-diffusive behavior in the Standard Map. European Physical Journal-Special Topics, JUN 2021. Web of Science Citations: 0.
PRADO, THIAGO DE LIMA; MACAU, ELBERT EINSTEIN NEHRER; LOPES, SERGIO ROBERTO. Detection of data corruption in stationary time series using recurrence microstates probabilities. European Physical Journal-Special Topics, JUN 2021. Web of Science Citations: 0.
VISCONDI, THIAGO F.; GRIGOLO, ADRIANO; CALDAS, IBERE L.; MENEGHINI, JULIO R. Slippery-sticky transition of interfacial fluid slip. Physics of Fluids, v. 33, n. 6 JUN 2021. Web of Science Citations: 0.
PROTACHEVICZ, PAULO R.; HANSEN, MATHEUS; IAROSZ, KELLY C.; CALDAS, IBERE L.; BATISTA, ANTONIO M.; KURTHS, JURGEN. Emergence of Neuronal Synchronisation in Coupled Areas. FRONTIERS IN COMPUTATIONAL NEUROSCIENCE, v. 15, APR 22 2021. Web of Science Citations: 0.
SILVEIRA, F. E. M.; CAMARGO, R. S.; CALDAS, I. L. Concentration discontinuity of alkalies at high pressures. Physics Letters A, v. 395, APR 16 2021. Web of Science Citations: 0.
VIANA, R. L.; CALDAS, I. L.; SZEZECH JR., J. D.; BATISTA, A. M.; ABUD, C. V.; SCHELIN, A. B.; MUGNAINE, M.; SANTOS, M. S.; LEAL, B. B.; BARTOLONI, B.; MATHIAS, A. C.; GOMES, J. V.; MORRISON, P. J. Transport Barriers in Symplectic Maps. Brazilian Journal of Physics, APR 2021. Web of Science Citations: 0.
PEREIRA, F. A. C.; TOUFEN, D. L.; GUIMARAES-FILHO, Z. O.; CALDAS, I. L.; VIANA, R. L.; GENTLE, K. W. Coexistence of turbulence regimes in the Texas Helimak. Physics of Plasmas, v. 28, n. 3 MAR 2021. Web of Science Citations: 0.
RUZISKA, FLAVIA M.; CALDAS, IBERE L. Synchronization and attractors in a model simulating social jetlag. CHAOS SOLITONS & FRACTALS, v. 144, MAR 2021. Web of Science Citations: 0.
RAPHALDINI, BRENO; MEDEIROS, EVERTON S.; CIRO, DAVID; FRANCO, DANIEL RIBEIRO; TRINDADE, RICARDO I. F. Geomagnetic reversals at the edge of regularity. PHYSICAL REVIEW RESEARCH, v. 3, n. 1 FEB 18 2021. Web of Science Citations: 0.
MUGNAINE, MICHELE; BATISTA, ANTONIO M.; CALDAS, IBERE L.; SZEZECH JR, JOSE D.; DE CARVALHO, RICARDO EGYDIO; VIANA, RICARDO L. Curry-Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems. Chaos, v. 31, n. 2 FEB 2021. Web of Science Citations: 1.
REIS, ADRIANE S.; IAROSZ, KELLY C.; FERRARI, FABIANO A. S.; CALDAS, IBERE L.; BATISTA, ANTONIO M.; VIANA, RICARDO L. Bursting synchronization in neuronal assemblies of scale-free networks. CHAOS SOLITONS & FRACTALS, v. 142, JAN 2021. Web of Science Citations: 0.
DE SOUZA, SILVIO L. T.; BATISTA, ANTONIO M.; CALDAS, IBERE L.; IAROSZ, KELLY C.; SZEZECH JR, JOSE D. Dynamics of epidemics: Impact of easing restrictions and control of infection spread. CHAOS SOLITONS & FRACTALS, v. 142, JAN 2021. Web of Science Citations: 0.
DE OLIVEIRA, VITOR M.; SOUSA-SILVA, PRISCILLA A.; CALDAS, IBERE L. Order-chaos-order and invariant manifolds in the bounded planar Earth-Moon system. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 132, n. 11-12 DEC 2020. Web of Science Citations: 0.
MUGNAINE, MICHELE; BATISTA, ANTONIO M.; CALDAS, IBERE L.; SZEZECH JR, JOSE D.; VIANA, RICARDO L. Ratchet current in nontwist Hamiltonian systems. Chaos, v. 30, n. 9 SEP 2020. Web of Science Citations: 0.
SILVA, I. M.; SCHELIN, A. B.; VIANA, R. L.; CALDAS, I. L. Transport of blood particles: Chaotic advection even in a healthy scenario. Chaos, v. 30, n. 9 SEP 2020. Web of Science Citations: 0.
DE SOUSA, M. C.; DOVEIL, F.; ELSKENS, Y.; CALDAS, I. L. Wave-particle interactions in a long traveling wave tube with upgraded helix. Physics of Plasmas, v. 27, n. 9 SEP 2020. Web of Science Citations: 0.
DOS SANTOS, VAGNER; BORGES, FERNANDO S.; IAROSZ, KELLY C.; CALDAS, IBERE L.; SZEZECH, J. D.; VIANA, RICARDO L.; BAPTISTA, MURILO S.; BATISTA, ANTONIO M. Basin of attraction for chimera states in a network of Rossler oscillators. Chaos, v. 30, n. 8 AUG 2020. Web of Science Citations: 0.
CONINCK, JOSE C. P.; FERRARI, FABIANO A. S.; REIS, ADRIANE S.; IAROSZ, KELLY C.; CALDAS, IBERE L.; BATISTA, ANTONIO M.; VIANA, RICARDO L. Network properties of healthy and Alzheimer brains. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 547, JUN 1 2020. Web of Science Citations: 0.
MARTINS DE OLIVEIRA, VITOR; CIRO, DAVID; CALDAS, IBERE LUIZ. Dynamical trapping in the area-preserving Henon map. European Physical Journal-Special Topics, v. 229, n. 8, SI, p. 1507-1516, MAY 2020. Web of Science Citations: 1.
RAPHALDINI, BRENO; CIRO, DAVID; MEDEIROS, EVERTON S.; MASSAROPPE, LUCAS; TRINDADE, RICARDO I. F. Evidence for crisis-induced intermittency during geomagnetic superchron transitions. Physical Review E, v. 101, n. 2 FEB 12 2020. Web of Science Citations: 0.
RAPHALDINI, BRENO; MEDEIROS, EVERTON; RAUPP, CARLOS F. M.; TERUYA, ANDRE SEIJI. A New Mechanism for Maunder-like Solar Minima: Phase Synchronization Dynamics in a Simple Nonlinear Oscillator of Magnetohydrodynamic Rossby Waves. Astrophysical Journal Letters, v. 890, n. 1 FEB 10 2020. Web of Science Citations: 0.
FERREIRA, LEONARDO N.; VEGA-OLIVEROS, DIDIER A.; ZHAO, LIANG; CARDOSO, MANOEL F.; MACAU, ELBERT E. N. Global fire season severity analysis and forecasting. Computers & Geosciences, v. 134, JAN 2020. Web of Science Citations: 1.
LOPEZ, ALVARO G.; IAROSZ, KELLY C.; BATIST, ANTONIO M.; SEOANE, JESUS M.; VIANA, RICARDO L.; SANJUAN, MIGUEL A. F. The role of dose density in combination cancer chemotherapy. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 79, DEC 2019. Web of Science Citations: 0.
MATHIAS, A. C.; MUGNAINE, M.; SANTOS, M. S.; SZEZECH, JR., J. D.; CALDAS, I. L.; VIANA, R. L. Fractal structures in the parameter space of nontwist area-preserving maps. Physical Review E, v. 100, n. 5 NOV 18 2019. Web of Science Citations: 0.
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, THERE L.; TEL, TAMAS; FEUDEL, ULRIKE. State-dependent vulnerability of synchronization. Physical Review E, v. 100, n. 5 NOV 4 2019. Web of Science Citations: 0.
DIAZ, I, GABRIEL; PALMERO, MATHEUS S.; CALDAS, IBERE LUIZ; LEONEL, EDSON D. Diffusion entropy analysis in billiard systems. Physical Review E, v. 100, n. 4 OCT 7 2019. Web of Science Citations: 0.
HANSEN, MATHEUS; CIRO, DAVID; CALDAS, IBERE L.; LEONEL, EDSON D. Dynamical thermalization in time-dependent billiards. Chaos, v. 29, n. 10 OCT 2019. Web of Science Citations: 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 AUG 2019. Web of Science Citations: 0.
GUSSO, ANDRE; VIANA, RICARDO L.; MATHIAS, AMANDA C.; CALDAS, IBERE L. Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes. CHAOS SOLITONS & FRACTALS, v. 122, p. 6-16, MAY 2019. Web of Science Citations: 3.
PEREIRA, F. A. C.; SOKOLOV, I. M.; TOUFEN, D. L.; GUIMARAES-FILHO, Z. O.; CALDAS, I. L.; GENTLE, K. W. Statistical properties of intermittent bursts in the Texas Helimak. Physics of Plasmas, v. 26, n. 5 MAY 2019. Web of Science Citations: 0.
PROTACHEVICZ, PAULO R.; BORGES, FERNANDO S.; LAMEU, EWANDSON L.; JI, PENG; IAROSZ, KELLY C.; KIHARA, ALEXANDRE H.; CALDAS, LBERE L.; SZEZECH JR, JOSE D.; BAPTISTE, MURILO S.; MACAU, ELBERT E. N.; ANTONOPOULOS, CHRIS G.; BATISTA, ANTONIO M.; KURTHSW, JUERGEN. Bistable Firing Pattern in a Neural Network Model. FRONTIERS IN COMPUTATIONAL NEUROSCIENCE, v. 13, APR 5 2019. Web of Science Citations: 2.
SANTOS, MOISES S.; PROTACHEVICZ, PAULO R.; IAROSZ, KELLY C.; CALDAS, IBERE L.; VIANA, RICARDO L.; BORGES, FERNANDO S.; REN, HAI-PENG; SZEZECH, JR., JOSE D.; BATISTA, ANTONIO M.; GREBOGI, CELSO. Spike-burst chimera states in an adaptive exponential integrate-and-fire neuronal network. Chaos, v. 29, n. 4 APR 2019. Web of Science Citations: 0.

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