Quasi-periodic states in coupled rings of cells

Antoneli, Fernando; Dias, Ana Paula S.; Pinto, Carla M. A.

doi:10.1016/j.cnsns.2009.05.035

Cited by 11 publications

(22 citation statements)

References 24 publications

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“…We compute a partial bifurcation diagram and the corresponding dynamical states in each bifurcating branch. The bifurcation scenario is similar to the one suggested in [15] and [2,3], for the first three Hopf points, and then it is extended to the region where chaos is observed. Period-doubling and halving-period bifurcations seem to take place, providing exciting dynamical features.…”

Section: Discussionmentioning

confidence: 53%

“…(1) The dynamical behavior of system 5 is much more complex than the one found in [2][3][4]29], for the same network of two coupled rings with Z 3 × Z 5 symmetry, but with simpler internal dynamics for each cell. Thus, the presence of symmetry constrains the dynamical behavior of the cells in each of the rings, but the resonance of the solutions seems to be strongly dependant of the choice of the vector field.…”

Section: Discussionmentioning

confidence: 99%

“…(3) The relaxation oscillations in the present study do not produce the curious phenomena, namely the behavior shown in Figs. 9 and 10 of [2], presented first in [15] and studied further in [3], for the Z 3 × Z 5 symmetric case. Again, this may depend on the choice of the vector field.…”

Section: Discussionmentioning

confidence: 99%

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Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

Pinto

2014

Nonlinear Dyn

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We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a "buffer" cell, with Z 3 × Z 5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

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Section: Discussionmentioning

confidence: 53%

Section: Discussionmentioning

confidence: 99%

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Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

Pinto

2014

Nonlinear Dyn

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“…This formalism frees the researcher of the details of the dynamics of each node and allows him to focus only on the network structure. Nevertheless, as was pointed before by Antoneli et al [2010], Pinto [2012Pinto [ , 2014, there are exotic features that cannot be explained solely by the network architecture and seem to be explained by the internal dynamics of each node (or cell).…”

Section: Introductionmentioning

confidence: 99%

“…A dynamically evolving network may exhibit distinct dynamical features, from synchronized states [Pikovsky et al, 2003;Stewart & Parker, 2007;Aguiar et al, 2011], phase locking [Pikovsky et al, 2003], resonance, quasiperiodicity, and other complex patterns [Huxter et al, 2003;Ikegaya et al, 2004;Antoneli et al, 2010;Pinto, 2012]. Synchronized states are extremely important in daily life [Zhu et al, 2013].…”

Section: Introductionmentioning

confidence: 99%

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

Pinto

2015

Int. J. Bifurcation Chaos

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We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z 3 × Z 5 cyclic symmetry group. The complex derivative D α±β ,withα, β ∈ R + is a generalization of the concept of integer order derivative, where α =1,β =0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β =0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈{0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

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