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Botella-Soler, V., Oteo, J. A., & Ros, J. (2012). Coexistence of periods in a bifurcation. Chaos Solitons Fractals, 45(5), 681–686.
Abstract: A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley-Gradwell-Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
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Botella-Soler, V., & Glendinning, P. (2012). Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems. EPL, 97(5), 50004–5pp.
Abstract: We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same network (polysynchronous states). These systems may have implications for the evolutionary emergence of polysynchrony and hierarchical networks in physical or biological systems modeled by adaptive networks.
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Botella-Soler, V., Castelo, J. M., Oteo, J. A., & Ros, J. (2011). Bifurcations in the Lozi map. J. Phys. A, 44(30), 305101–14pp.
Abstract: We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.
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Botella-Soler, V., Oteo, J. A., Ros, J., & Glendinning, P. (2013). Lyapunov exponent and topological entropy plateaus in piecewise linear maps. J. Phys. A, 46(12), 125101–26pp.
Abstract: We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.
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Botella-Soler, V., Valderrama, M., Crepon, B., Navarro, V., & Le Van Quyen, M. (2012). Large-Scale Cortical Dynamics of Sleep Slow Waves. PLoS One, 7(2), e30757–10pp.
Abstract: Slow waves constitute the main signature of sleep in the electroencephalogram (EEG). They reflect alternating periods of neuronal hyperpolarization and depolarization in cortical networks. While recent findings have demonstrated their functional role in shaping and strengthening neuronal networks, a large-scale characterization of these two processes remains elusive in the human brain. In this study, by using simultaneous scalp EEG and intracranial recordings in 10 epileptic subjects, we examined the dynamics of hyperpolarization and depolarization waves over a large extent of the human cortex. We report that both hyperpolarization and depolarization processes can occur with two different characteristic time durations which are consistent across all subjects. For both hyperpolarization and depolarization waves, their average speed over the cortex was estimated to be approximately 1 m/s. Finally, we characterized their propagation pathways by studying the preferential trajectories between most involved intracranial contacts. For both waves, although single events could begin in almost all investigated sites across the entire cortex, we found that the majority of the preferential starting locations were located in frontal regions of the brain while they had a tendency to end in posterior and temporal regions.
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