Publications (57)79.07 Total impact
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ABSTRACT: We investigate a threedimensional discretetime dynamical system, described by a threedimensional map derived from a continuoustime HindmarshRose neuron model by the forward Euler method. For a fixed integration step size, we report a twodimensional parameterspace for this system, where periodic structures, the socalled Arnold tongues, can be seen with periods organized in a Farey tree sequence. We also report possible modifications in this parameterspace, as a function of the integration step size.  [Show abstract] [Hide abstract]
ABSTRACT: We report parameter planes displaying dynamical behaviors of the fourvariable, fourparameter LorenzStenflo system, which describes the time evolution of nonlinear lowfrequency shortwavelength gravity wave disturbance in a rotating atmosphere. All the six parameter combinations two by two are considered. By using Lyapunov exponents spectra to characterize the dynamics of the LorenzStenflo system, we show that hyperchaos is not present. Chaotic, quasiperiodic, periodic, and equilibrium point regions are delimited in the considered parameter planes.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate a parameter plane of a set of three autonomous, tenparameter, firstorder nonlinear ordinary differential equations, which models a tritrophic food web system. By using Lyapunov exponents, bifurcation diagrams, and trajectories in the phasespace, to numerically characterize the dynamics of the model in a parameter plane, we show that it presents typical periodic structures embedded in a chaotic region, forming a spiral structure that coils up around a focal point while periodadding bifurcations take place. 
Article: Delimiting hyperchaotic regions in parameter planes of a 5D continuoustime dynamical system
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ABSTRACT: Different ways to numerically characterize hyperchaotic regions in parameter planes of a 5D continuoustime nonlinear dynamical system are utilized in this work. The method considers the three largest Lyapunov exponents, to construct twodimensional parameter planes colorful plots. In some these plots different levels of hyperchaos are represented by a continuously changing yellow to red scale, while in other different colors mean different number of positive Lyapunov exponents.  [Show abstract] [Hide abstract]
ABSTRACT: We report on the dynamics in a parameter plane of a continuoustime damped system driven by a periodic forcing. The dynamics is characterized by considering the Lyapunov exponents spectrum and conventional bifurcation diagrams, to discriminate periodic, quasiperiodic, and chaotic behaviors for each point in this parameter plane, according two parameters are simultaneously varied. Periodic structures born in a quasiperiodic region and embedded in a chaotic region, the socalled Arnold tongues, are observed. We show that the Arnold tongues periodic distribution is highly organized in a mixed set of two periodadding sequences. Other three typical periodic structures born and embedded in a chaotic region were observed, also individually organized in a mixed set of two periodadding sequences.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate periodicity suppression in twodimensional parameterspaces of discreteand continuoustime nonlinear dynamical systems, modeled respectively by a twodimensional map and a set of three firstorder ordinary differential equations. We show for both cases that, by varying the amplitude of an external periodic forcing with a fixed angular frequency, windows of periodicity embedded in a chaotic region may be totally suppressed.  [Show abstract] [Hide abstract]
ABSTRACT: We report results of a numerical investigation on a twodimensional crosssection of the parameterspace of a set of three autonomous, eightparameter, firstorder ordinary differential equations, which models tumor growth. The model considers interaction between tumor cells, healthy tissue cells, and activated immune system cells. By using Lyapunov exponents to characterize the dynamics of the model in a particular parameter plane, we show that it presents typical selforganized periodic structures embedded in a chaotic region, that were before detected in other models. We show that these structures organize themselves in two independent ways: (i) as spirals that coil up toward a focal point while undergoing periodadding bifurcations and, (ii) as a sequence with a welldefined law of formation, constituted by two mixed periodadding bifurcation cascades.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate analytically and numerically the dynamics of the Rikitake system. The RouthHurwitz criterion is used to study the stability of the equilibrium points of the differential equation system model, as functions of two parameters. The dynamics of the model are numerically studied using diagrams that associate colors to the largest Lyapunov exponent value, in twodimensional parameter spaces. Additionally, phasespace plots and bifurcation diagrams are used to distinguish periodic and chaotic attractors.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate changes in periodicity, and even its suppression, by external periodic forcing in different twodimensional maps, namely the Hénon map and the sine square map. By varying the amplitude of a periodic forcing with a fixed angular frequency, we show through numerical simulations in parameterspaces that changes in periodicity may take place. We also show that windows of periodicity embedded in a chaotic region may be totally suppressed.  [Show abstract] [Hide abstract]
ABSTRACT: A transition from Mandelbrotlike sets to Arnold tongues is characterized via a coupling of two nonidentical quadratic maps proposed by us. A twodimensional parameterspace considering the parameters of the individual quadratic maps was used to demonstrate numerically the event. The location of the parameter sets where NaimarkSacker bifurcations occur, which is exactly the place where Arnold tongues of arbitrary periods are born, was computed analytically.  [Show abstract] [Hide abstract]
ABSTRACT: Three twodimensional parameter planes of a threeparameter, threedimensional set of autonomous nonlinear firstorder differential equations used to model the A2 symmetric flow are investigated. This is done by using the three twodimensional cross sections of the threedimensional parameterspace generated by the model. We show that regardless of the twoparameter set considered in the parameter plane plots, all the diagrams present periodic structures embedded in a large chaotic region. We also show that these periodic structures organize themselves in different ways, including sequences whose periods have a welldefined law of formation that can be written in a closed form, and sequences organized in periodadding bifurcation cascades.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark—Sacker bifurcations of stable period1, period2, and period3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to modelocked states and to chaotic states, and from chaotic to hyperchaotic states.  [Show abstract] [Hide abstract]
ABSTRACT: Parameter plane plots related to a periodically forced compound Kortewegde VriesBurgers system, which is modeled by a thirdorder partial differential equation, are reported. It is shown that typical periodic structures embedded in a chaotic region in these parameter planes, organize themselves in different ways. There are bifurcation sequences whose periods have a welldefined law of formation, that may be written in a closed form, and there are bifurcation sequences selforganized in periodadding cascades.  [Show abstract] [Hide abstract]
ABSTRACT: We report the results of our numerical investigation on a parameter plane of a set of six autonomous fiveparameter firstorder ordinary differential equations, namely a coupling of two identical chaotic Rössler oscillators. Using the Lyapunov exponents spectrum to characterize the dynamics of the model in a parameter plane that considers the asymmetry and the strength of the coupling, we show that this particular parameter plane presents malformed shrimpshaped periodic structures embedded in a hyperchaotic region, which are selforganized in periodadding bifurcation cascades.  [Show abstract] [Hide abstract]
ABSTRACT: We report some results indicating changes in the observed dynamics of the Rössler model under the influence of external sinusoidal forcing. By varying the control parameters of the external sinusoidal forcing, namely the amplitude and the angular frequency, we show, through numerical simulations which include parameter planes and Lyapunov exponents, that the external forcing can produce both chaosorder and orderchaos transitions. We also show that the sinusoidal forcing may generate hyperchaos.  [Show abstract] [Hide abstract]
ABSTRACT: This work reports twodimensional parameter space plots, concerned with a threedimensional Hopfieldtype neural network with a hyperbolic tangent as the activation function. It shows that typical periodic structures embedded in a chaotic region, called shrimps, organize themselves in two independent ways: (i) as spirals that individually coil up toward a focal point while undergo periodadding bifurcations and, (ii) as a sequence with a welldefined law of formation, constituted by two different periodadding sequences inserted between.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate periodicity suppression by an external periodic forcing in different flows, each modeled by a set of three autonomous nonlinear firstorder ordinary differential equations. By varying the amplitude of a sinusoidal forcing with a fixed angular frequency, we show through numerical simulations, including parameter planes plots, phasespace portraits, and the largest Lyapunov exponent, that windows of periodicity embedded in chaotic regions may be totally suppressed. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772968] 
Article: Hopfield neural network: The hyperbolic tangent and the piecewiselinear activation functions
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ABSTRACT: This paper reports twodimensional parameterspace plots for both, the hyperbolic tangent and the piecewiselinear neuron activation functions of a threedimensional Hopfield neural network. The plots obtained using both neuron activation functions are compared, and we show that similar features are present on them. The occurrence of selforganized periodic structures embedded in chaotic regions is verified for the two cases.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a situation in which the two parameters of a Hénon map are modulated by the output of another Hénon map. Two cases are considered. Firstly, we investigate the behavior of the Hénon map when its parameters are modulated by another Hénon map, this last working in a high dissipative regime. Secondly, we use a Hénon map working in a low dissipative regime as the modulation. We show that, regardless of the considered case, multistability can be suppressed by the modulation.Highlights► We consider the modulation of the parameters of a Hénon map, by a second Hénon map. ► We consider the modulator Hénon map working in a high dissipative regime. ► The modulator Hénon map working in a low dissipative regime also is considered. ► Regardless the modulator regime, multistability may be suppressed in the Hénon map.  [Show abstract] [Hide abstract]
ABSTRACT: Some twodimensional parameterspace diagrams are numerically obtained by considering the largest Lyapunov exponent for a fourdimensional thirteenparameter Hindmarsh—Rose neuron model. Several different parameter planes are considered, and it is shown that depending on the combination of parameters, a typical scenario can be preserved: for some choice of two parameters, the parameter plane presents a combshaped chaotic region embedded in a large periodic region. It is also shown that there exist regions close to these combshaped chaotic regions, separated by the comb teeth, organizing themselves in periodadding bifurcation cascades.
Publication Stats
328  Citations  
79.07  Total Impact Points  
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Institutions

20002015

Universidade do Estado de Santa Catarina
 Departamento de Física
Joinville, Santa Catarina, Brazil


1998

Federal University of Santa Catarina
Nossa Senhora do Destêrro, Santa Catarina, Brazil
