Professor

Mini currículo

Doutor em Física pela Universidade Federal do Paraná, com ênfase em Física Teórica. Tese versando sobre Bifurcações, multiestabilidade e sincronização caótica em sistemas dinâmicos discretos.

Área de interesse

Dinâmica não linear e sistemas dinâmicos não lineares. O interesse principal está no estudo da dinâmica de sistemas a tempo contínuo, modelados por equações diferenciais, e sistemas a tempo discreto, modelados por mapas. Também há interesse na investigação de sincronização caótica e controle de caos em sistemas dinâmicos em geral.

Publicações

Artigos científicos publicados/aceitos/submetidos/em preparação

Manchein, C., Rech, P.C., Coupling dynamics in sinusoidally driven FitzHugh-Nagumo neurons: Analyzing chaos suppression and coexisting attracting sets, em preparação.

Rech, P.C., Multistability and Organization of Chaos and Quasiperiodicity in a Memristor-Based Shimizu-Morioka Oscillator Under Two-Frequency Excitation, submetido para publicação

Bosco, N.D., Rech, P.C., Beims, M.W., Manchein, C., Influence of sinusoidal forcing on the master FitzHugh–Nagumo neuron model and global dynamics of a unidirectionally coupled two-neuron system, Chaos, vol. 34, 093124, 2024.

Sagás, J.C., Recco, A.A.C., Rech, P.C., Chaos, periodicity, and multistability in a plasma oscillator forced by a non-sinusoidal wave function, Fundamental Plasma Physics, vol. 12, 100072, 2024.

Rech, P.C., Complex Dynamics of a Linear Coupling of Two Chaotic Lorenz Systems, Brazilian Journal of Physics, vol. 54, 15, 2024.

Soares, I.L., Krol, M.F., Rech, P.C., Coexisting attractors and basins of attraction of an extended forced Duffing oscillator, European Physical Journal B, vol. 97, 71, 2024.

Manchein, C., Rech, P.C., Effects of external stimuli on the dynamics of deterministic and stochastic Hindmarsh-Rose neuron models, European Physical Journal B, vol. 97, 113, 2024.

Recco, A.A.C., Sagás, J.C., Rech, P.C., Multistability, period-adding, and fractality in a plasma oscillator, Physics of Plasmas, vol. 30, 112301, 2023.

Silva, C.F., Rech, P.C, Chaos suppression, hyperchaos, period-adding, and discontinuous spirals in a bidirectional coupling of Lorenz systems, European Physical Journal B, vol. 96, 4, 2023.

Francisco, B.B.T., Rech, P.C., Multistability, period-adding, and spirals in a snap system with exponential nonlinearity, European Physical Journal B, vol. 96, 63, 2023.

Rech, P.C., Multistability in a Circulant Dynamical System, Communications in Advanced Mathematical Sciences, vol. 6, 98-103, 2023.

Wiggers, V., Rech, P.C., On the dynamics of a Van der Pol-Duffing snap system, European Physical Journal B, vol. 95, 1-6, 2022.

Da Silva, A., Pati, N.C., Rech, P.C., Multistability and period-adding in a logarithmic Lorenz system, International Journal of Modern Physics C, vol. 33, 2250062, 2022.

Rech, P.C., Self-excited and hidden attractors in a multistable jerk system, Chaos Solitons & Fractals, vol. 164, 112614, 2022.

Rech, P.C., Periodicity suppression and period-adding caused by a parametric excitation in the Lorenz system, European Physical Journal B, vol. 95, 169, 2022.

Da Silva, A., Rech, P.C., On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network, Communications in Advanced Mathematical Sciences, vol. 5, 92-98, 2022.

Rech, P.C., Dynamics of a Four-Dimensional System with Cubic Nonlinearities, International Journal of Bifurcation and Chaos, vol. 31, 2150012, 2021.

Rech, P.C., Chaos suppression instigated by a hyperbolic sine nonlinearity in the Chen system, International Journal of Modern Physics C, vol. 32, 2150133, 2021.

Francisco, B.B.T., Rech, P.C., Exploring the Parameter-Space of a Generalized Four-dimensional Rössler System, Brazilian Journal of Physics, vol. 51, 1472-1477, 2021.

Pati N.C., Rech P.C., Layek G.C., Multistability for nonlinear acoustic-gravity waves in a rotating atmosphere, Chaos, vol. 31, 023108, 2021.

Rech P.C., Hyperchaos and multistability in a four-dimensional financial mathematical model, Journal of Applied Nonlinear Dynamics, vol. 10, 211-218, 2021.

Rech P.C., Dynamics of a four-dimensional system with cubic nonlinearities, International Journal of Bifurcation and Chaos, vol. 31, 2150012, 2021.

Rech P.C., Multistability in a periodically forced Brusselator, Brazilian Journal of Physics, vol. 51, 144-147, 2021.

Pati N.C., Rech P.C., Dynamics of a high-order generalized Lorenz model for magnetoconvection, International Journal of Bifurcation and Chaos, vol. 30, 2050187, 2020.

Rech P.C., On the dynamics of a modified Lorenz-Stenflo system, International Journal of Modern Physics C, vol. 31, 2050104, 2020.

Rech P.C., On Two Discrete-Time Counterparts of a Continuous-Time Prey-Predator Model, Brazilian Journal of Physics, vol. 50, 119-123, 2020.

Rech P.C., Dua S., Pati N.C., Multistability and bubbling route to chaos in a deterministic model for geomagnetic field reversals, International Journal of Bifurcation and Chaos, vol. 29, 1930034, 2019.

Ramos J.C., Rech P.C., Delimitation of Hyperchaotic Regions in Parameter Planes of a Four-dimensional Dynamical System, Journal of Discontinuity Nonlinearity and Complexity, vol. 8, 459-465, 2019.

Rech P.C., Nonlinear dynamics of two discrete-time versions of the continuous-time Brusselator model, International Journal of Bifurcation and Chaos,  vol. 29, 950142, 2019.

Daumann C.C, Rech P.C., Hyperchaos in convection with the Cattaneo-Christov heat-flux model, European Physical Journal B, vol. 92, 110, 2019.

Rech P.C., Organization of the dynamics in the parameter-space of a glycolysis discrete-time mathematical model, Journal of Mathematical Chemistry, vol. 57, 632, 2019.

Wiggers V., Rech P.C., On symmetric and asymmetric Van der Pol-Duffing oscillators, European Physical Journal B, vol. 91, 144, 2018.

da Silva A., Rech P.C., Numerical investigation concerning the dynamics in parameter planes of the Ehrhard-Müller System, Chaos Solitons & Fractals, vol. 110, 152-157, 2018.

Felício C.C., Rech P.C., On the dynamics of five- and six-dimensional Lorenz models, Journal of Physics Communications, vol. 2, 025028, 2018.

Rech P.C., Hyperchaos and quasiperiodicity from a four-dimensional system based on Lorenz system, European Physical Journal B, vol. 90, 251, 2017.

Wiggers V., Rech P.C., Multistability and organization of periodicity in a Van der Pol-Duffing oscillator, Chaos Solitons & Fractals, vol. 103, 632-637, 2017.

Wiggers V., Rech P.C., Chaos, periodicity , and quasiperiodicity in a radio-physical oscillator, International Journal of Bifurcation and Chaos, vol. 27(7), 1730023, 2017.

Rech P.C., How to embed shrimps in parameter planes of the Lorenz system, Physica Scripta, vol. 92(4), 045201, 2017.

Prants F.G., Rech P.C., Complex dynamics of a three-dimensional continuous-time autonomous dynamical system, Mathematics and Computers in Simulation, vol. 136, 132-139, 2017.

Borghezan M., Rech P.C., Chaos and periodicity in Valli's model for El Niño, Chaos Solitons & Fractals, vol. 97, 15-18, 2017.

da Silva A., Rech P.C., Chaos and periodicity in a discrete-time Baier-Sahle model, Asian Journal of Mathematics and Computer Research,
vol. 15(2), 123-130, 2017.

Rech P.C., On the dynamics of high-order Lorenz-Stenflo system, Physica Scripta, vol. 91(12), 125201, 2016.

Rech P.C., Quasiperiodicity and chaos in the Nosé-Hoover oscillator, International Journal of Bifurcation and Chaos, vol. 26(10), 1650170, 2016.

Rech P.C., Spiral organization of periodic structures in the Lorenz-Stenflo system, Physica Scripta, vol. 91, 075201, 2016.

Prants F.G., Rech P.C., Suppression of periodic structures and the onset of hyperchaos in a parameter-space of the Baier-Sahle flow, Chaos Solitons & Fractals, vol. 83, p. 105–111, 2016.

Prants F.G., Rech P.C., Switching between the Lorenz system and the Rössler oscillator, Journal of Applied Physical Science International, vol. 5, p. 42-49, 2016.

Rech, P.C., Period-adding in a three-dimensional dynamical system, Asian Journal of Mathematics and Computer Research, vol. 7, p. 1-8, 2016.

Rech P.C., Period-Adding Structures in the Parameter-Space of a Driven Josephson Junction, International Journal of Bifurcation and Chaos, vol. 25, 1530035, 2015.

Rech, P.C., On the dynamics in parameter planes of the Lorenz-Stenflo system, Physica Scripta, Vol. 90, 115201, 2015.

Felício C.C., Rech P.C., Arnold tongues and the Devil's staircase in a discrete-time Hindmarsh-Rose neuron model, Physics Letters A, vol. 379, p. 2845-2847, 2015.

da Silva R.A., Rech P.C., Spiral periodic structures in a parameter plane of an ecological model, Applied Mathematics and Computation, v. 254, p. 9-13, 2015.

Rech P.C., Period-adding and Spiral Organization of Periodicity in a Hopfield Neural Network, International Journal of Machine Learning and Cybernetics, v. 6, p. 1-6, 2015.

Rech P.C., Delimiting hyperchaotic regions in parameter planes of continuous-time dynamical systems, Applied Mathematics and Computation, v. 247, p. 13, 2014.

Prants F.G., Rech P.C., Organization of periodic structures in a damped-forced oscillator, European Physical Journal B, v. 87, 196, 2014

Rech P.C., Cleaning the periodicity in discrete- and continuous-time nonlinear dynamical systems, International Journal of Bifurcation and Chaos, v. 24(7), 1430020, 2014.

Stegemann C., Rech P.C., Organization of chaos and periodicity in a three-dimensional cancer model, International Journal of Bifurcation and Chaos, v. 24(2), 1450023, 2014.

da Silva R.A., Rech P.C., A parameter space analysis of the Rikitake system, Chinese Physics Letters, v. 30, 120501, 2013.

Endler A., Rech P.C., From Mandelbrot-like sets to Arnold tongues, Applied Mathematics and Computation, v. 222, p. 559-563, 2013.

Rech P.C., Nonlinear dynamics investigation in parameter planes of a periodically forced compound KdV-Burgers equation, European Physical Journal B, v. 86, 356, 2013.

Rech P.C., The parameter-space of the three-parameter A2 symmetric flow, Applied Mathematics and Computation, v. 220, p. 208-212, 2013.

Rech P.C., The dynamics of a symmetric coupling of three modified quadratic maps, Chinese Physics B, v. 22, 080202, 2013.

Rech P.C., Changes in the dynamics of two-dimensional maps by external forcing, Physics Letters A, v. 377, p. 1881, 2013.

Prants W.T., Rech P.C., The organization of periodicity and hyperchaos in an asymmetric coupling of two chaotic R¨ossler oscillators, Physica Scripta, v. 88, 015001, 2013.

Mathias A.C. , Rech P.C., Changes in the dynamics of a Rössler oscillator by an external forcing, Chinese Physics Letters, v. 30, 030502, 2013.

Mathias A.C., Rech P.C., Periodicity suppression in continuous-time dynamical systems by external forcing, Chaos: An Interdisciplinary Journal of Nonlinear Science, v. 22, 043147, 2012.

Mathias A.C. , Rech P.C., Hopfield neural network: the hyperbolic tangent and the piecewise-linear activation functions, Neural Networks, vol. 34, p. 42, 2012.

Rech P.C., Dynamics in the parameter-space of a neuron model, Chinese Physics Letters, vol. 29(6), 060506, 2012.

Albuquerque H.A., Rech P.C., Spiral periodic structure inside chaotic region in parameter-space of a Chua circuit, International Journal of Circuit Theory and Applications, vol. 40, p. 189, 2012.

Correia M.J., Rech, P.C., Numerical characterization of hyperchaotic states in parameter-space, Applied Mathematics and Computation, vol. 218, p. 6711, 2012.

Krüger T.S., Rech P.C., Dynamics of an erbium-doped fiber dual-ring laser, European Physical Journal D, v. 66(1), p. 12, 2012.

Casas G.A., Rech P.C., Multistability annihilation in the Hénon map through parameter modulation, Communications in Nonlinear Science and Numerical Simulation, v. 17, p. 2570, 2012.

Brugnago E.L., Rech, P.C., Chaos suppression in a sine square map through a nonlinear coupling, Chinese Physics Letters, v. 28, 110506, 2011.

Rech P.C., Chaos and hyperchaos in a Hopfield neural network, Neurocomputing, v. 74, p. 3361, 2011.

Stegemann C., Albuquerque H. A., Rubinger R. M., Rech P. C., Lyapunov exponent diagrams of a 4-dimensional circuit model, Chaos: An Interdisciplinary Journal of Nonlinear Science, v. 21, 033105, 2011.

Casas G.A., Rech P.C., A parametrically modulated H�non map, Journal of Physics: Conference Series, v. 285, 012001, 2011.

Correia M.J., Rech, P.C., Characterization of hyperchaotic states in the parameter-space of a modified Lorenz system, Journal of Physics: Conference Series, v. 285, 012017, 2011.

Rech, P.C., Dynamics of a neuron model in different two-dimensional parameter-spaces, Physics Letters A, v. 375, p.1461, 2011.

Casas G.A., Rech P.C., Numerical Study of a Three-Dimensional Hénon Map, Chinese Physics Letters, v. 28(1), 010203, 2011.

Correia M.J., Rech P.C., Hyperchaos in a new four-dimensional autonomous system, International Journal of Bifurcation and Chaos, v. 20(10), p.3295, 2010.

Rech, P.C., Self-similarities and period-adding in the parameter-space of a nonlinear resonant coupling process, International Journal of Nonlinear Science, v. 10(2), p.179, 2010.

Rech P.C., Beims M. W., Stability analysis under dilatation of coordinates, Journal of Physics: Conference Series, vol. 246, 012006, 2010.

Testoni G.E., Rech, P.C., Dynamics of a particular Lorenz type system, International Journal of Modern Physics C, vol. 21(7), p. 973, 2010.

Xavier J.C., Rech P.C., Chaos and hyperchaos in a symmetric coupling of three quadratic maps, Journal of Computational Interdisciplinary Sciences, v. 1(3), p. 225, 2010.

Stegemann C., Albuquerque H.A., Rech P.C., Some two-dimensional parameter spaces of a Chua system with cubic nonlinearity, Chaos: An Interdisciplinary Journal of Nonlinear Science, v. 20, 023103, 2010.

Xavier J.C., Rech P.C., Regular and chaotic dynamics in the Lorenz-Stenflo system, International Journal of Bifurcation and Chaos, v. 20, p.145, 2010.

Casas G.A., Rech P.C., Dynamics of asymmetric couplings of two H�non maps, International Journal of Bifurcation and Chaos, v. 20, p.153, 2010.

Rech P.C., Albuquerque H.A., A hyperchaotic Chua system, International Journal of Bifurcation and Chaos, v. 19, p. 3823, 2009.

Albuquerque H.A., Rech P.C., A Parameter-space of a Chua system with a smooth nonlinearity, International Journal of Bifurcation and Chaos, v. 19, p. 1351, 2009.

Rech P.C., A coupling of three quadratic maps, Chaos, Solitons and Fractals, v. 41, p. 1949, 2009.

Rosa C. , Correia M.J., Rech, P.C., Arnold tongues and quasiperiodicity in a prey predator model, Chaos, Solitons and Fractals, v. 40, p. 2041, 2009.

Albuquerque H.A., Rubinger R.M., Rech P.C., Self-similar structures in a 2D parameter-space of an inductorless Chua's circuit, Physics Letters A, v. 372, p. 4793, 2008.

Rech P.C., Chaos control in a discrete time system through asymmetric coupling, Physics Letters A, v. 372, p. 4434, 2008.

Rech, P.C., Naimark-Sacker bifurcations in a delay quartic map, Chaos, Solitons and Fractals, v. 37, p. 387, 2008.

Albuquerque, H.A., Rubinger, R.M., Rech, P.C., Theoretical and Experimental time series analysis of an inductorless Chua's circuit, Physica D v. 233, p. 66, 2007.

Rech, P.C., Gallas, J.A.C., Beims, M.W., Generation of quasiperiodic oscillations in pairs of coupled maps, Chaos, Solitons and Fractals v. 33, p. 1394, 2007.

Rech, P.C., Gallas, J.A.C., Beims, M.W., Basin size evolution between dissipative and conservative limits, Physical Review E v. 71, p. 17202, 2005.

Van Vessen M., Rech, P.C., Beims, M.W., Gallas, J.A.C., Freire J.A., da Luz M.G.E., Lind P.G., The dynamics of complex-amplitude norm-preserving lattices of coupled oscillators, Physica A v. 338, p. 537-543, 2004.

Rech, P.C., Beims, M.W., Gallas, J.A.C., Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps, Physica A v. 342, p. 351-355, 2004.

Rech, P.C., Gallas, J.A.C., Beims, M.W., Fractal and riddled basins: arithmetic signatures in the parameter space of two coupled quadratic maps, Physica A v. 295, p. 276-279, 2001.

Rech, P.C., Beims, M.W., Gallas, J.A.C., Discovering parameter values by measuring self-similar structures in the phase-space of dissipative systems with constant Jacobian, Europhysics Letters v. 49, p. 702-707, 2000.

Rech, P.C., Beims, M.W., Gallas, J.A.C., Recovering parameters from self-similar structures in phase-space of dissipatives systems with constant jacobian, Physica A v. 283, p. 252-252, 2000.

Rech, P.C., Gallas, M., Gallas, J.A.C., Rapidly converging bounds for the ground-state energy of hydrogenic atoms in superstrong magnetic fields, Physical Review Letters v. 62, p. 2198-2199, 1989.

Rech, P.C., Gallas, M., Gallas, J.A.C., Zeeman Diamagnetism in Hydrogen at arbitrary Field Strengths, Journal of Physics B v. 19, p. L215-L218, 1986.