Chaos in mesoscopic systems. Proceedings of the miniworkshop and Adriatico research conference
Part 1 Models and natural systems: chaos on many body quantum systems, C. Presilla et al atomic c... more Part 1 Models and natural systems: chaos on many body quantum systems, C. Presilla et al atomic clusters - laboratories for studying chaos and ergodicity, R.S. Berry concerning fluctuations in quantum chaos, G. Casati and B. Chirikov persistent fluctuations in globally coupled chaotic systems, G. Perez et al. Part 2 Artificial microstructures: order and chaos in a quantum system - semiclassical electron effusion theory of conductance through a microscopic junction, J.B. Delos et al breakdown of the law of large numbers in Josephson junction series arrays, D. Dominguez and H.A. Cerdeira antidot arrays - chaotic dynamics in magnetotransport experiments, D. Weiss and K. Richter. (Part contents).
In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our mai... more In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic.
The effect of a weak magnetic field on the diffusion of noninteracting electrons in a disordered ... more The effect of a weak magnetic field on the diffusion of noninteracting electrons in a disordered system is studied in a nonlinear a-model context. The effective Lagrangian describing the soft modes of the system in the weak field limit is derived. The result does not have the simple form that has been suggested by several authors. Therefore the crossover of the system under a weak perturbing magnetic field is not analogous to that found in spin systems.
We show the existence and stability of frozen splay states as well as temporally chaotic splay st... more We show the existence and stability of frozen splay states as well as temporally chaotic splay states in a coupled sine circle map lattice system using analytic and numerical techniques. The splay states are observed for very low values of the nonlinearity parameter, i.e., for circle maps which deviate very slightly from the shift map case. We also observe that, depending on the parameters of the system, the splay states bifurcate to mixed or chimera splay states, consisting of a mixture of splay and synchronised states, together with kinks in the phases of some of the maps and then to a globally synchronised state. We estimate the parameter regions where these pure states and the mixed states are seen. We also briefly show that similar spatial splay structures can exist in experimentally realisable systems like Josephson junction arrays and Hartley-like oscillator arrays.
Parameter and coupling estimation in small networks of Izhikevich’s neurons
Chaos: An Interdisciplinary Journal of Nonlinear Science
Nowadays, experimental techniques allow scientists to have access to large amounts of data. In or... more Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems that produce these data, appropriate analysis tools are needed. The Kalman filter is a frequently used technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. In this work, we test whether the UKF can also reconstruct the connectivity of small groups of coupled neurons when their links are either electrical or chemical synapses. In particular, we consider Izhikevich neurons and aim to infer which neurons influence each other, considering simulated spike trains as the experimental observations used by the UKF. First, we verify that the UKF can recover the parameters of a single neuron, even when the...
Chaos: An Interdisciplinary Journal of Nonlinear Science
We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Pr... more We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster, and chimera states. Here, we consider a network with two layers of Rössler chaotic oscillators as well as applications to multilayer networks of the chaotic jerk and Liénard oscillators. Intra-layer coupling is considered to be all to all in the case of Rössler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Liénard, inter-layer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in-depth study on the case of a network of Rössler oscillators using a master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster, and phase synchronization with amplification. For the case of Rössler oscillators, we note that there are also certain ...
Heuristic Active Learning for the Prediction of Epileptic Seizures Using Single EEG Channel
2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2018
Predicting epileptic seizure occurrence has long been a goal of the community surrounding it. Acc... more Predicting epileptic seizure occurrence has long been a goal of the community surrounding it. Accurate prediction, however, is still elusive. This work presents a modified pipeline for the training of seizure prediction systems which aims to attenuate the effects of current data labeling strategies - and consequent data mislabeling of samples that heavily affect classifiers that are trained on it. This paper also presents a seizure prediction system trained following the proposed pipeline, which improved our system’s performance by reducing its time-in-warning (TiW) by over 14%, while improving its prediction sensitivity to 72.4%, bringing its performance closer to the state-of-the-art performance (83.1% prediction sensitivity) for systems with similar TiW(41%) [1], while only requiring input from two scalp EEG electrodes-without making use of any variables external to the single EEG channels.
We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-R... more We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, ie the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of instantaneous local order parameter in two dimensions. We extend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of propagation of patterns in two dimensions.
This paper presents a simple Josephson-junction circuit with two parameters (inductance and capac... more This paper presents a simple Josephson-junction circuit with two parameters (inductance and capacitance) which can be tuned to represent different energy landscapes with different physical properties. By tuning this quantum circuit through external accessible elements we can move from two to three and more energy levels depending on the parameter setting. The inductance, the capacitance as well as the external voltage (driving terms) condition the number of relevant energy levels as well as the model to be used.
Synchronization Dynamics of Modified Relay-coupled Chaotic Systems
Journal of Applied Nonlinear Dynamics, 2018
Instituto de Fisica Teorica - UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz... more Instituto de Fisica Teorica - UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II
Synchronization structure of evolving epileptic networks using cross-entropy
The European Physical Journal Special Topics, 2018
Abstract In this paper we present connectivity patterns of evolving large scale epileptic network... more Abstract In this paper we present connectivity patterns of evolving large scale epileptic networks. We employed a cross-entropy measure in the frequency domain on EEG signals to infer the networks, before and during episodes of epileptic seizures. This measure allowed us to make a richer portrait about the node interactions on the graph and to identify emergent structures associated with the synchronization of brain activity. Our results points to a more complex scenario of network organization than the synchronized/unsynchronized dichotomy, with two main results: first, showing regions with unsynchronized (or independent) behavior, even during absence seizures, contradicting the concept of hypersynchrony. Furthermore, we explore the cross-entropy fluctuations along the seizure: a group of nodes became more similar over time while another group became more different, showing a complementary behaviour and different local brain activities. These results bring new questions about the spreading and the sustenance of the epileptic seizures and others synchronization phenomena in living systems.
The European Physical Journal Special Topics, 2016
In this work, we proposed a novel way to estimate phase-lag synchronization in coupled systems. T... more In this work, we proposed a novel way to estimate phase-lag synchronization in coupled systems. This approach was applied into two systems: a directed-coupled Rössler-Lorenz system and a network of Izhikevich neurons. For the former case, the phase-lag synchronization revealed an increase in complexity for the Lorenz subsystem components, when the coupling is activated. The opposite behavior was observed when the Izhikevich network were organized in a hierarchical way. Our results point out to emergent synchronism related to causal interactions in coupled complex systems.
We report on the bifurcation analysis of an extended Hindmarsh-Rose (eHR) neuronal oscillator. We... more We report on the bifurcation analysis of an extended Hindmarsh-Rose (eHR) neuronal oscillator. We prove that Hopf bifurcation occurs in this system, when an appropriate chosen bifurcation parameter varies and reaches its critical value. Applying the normal form theory, we derive a formula to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic flows. To observe this latter bifurcation and to illustrate its theoretical analysis, numerical simulations are performed. Hence, we present an explanation of the discontinuous behavior of the amplitude of the repetitive response as a function of system's parameters based on the presence of the subcritical unstable oscillations. Furthermore, the bifurcation structures of the system are studied, with special care on the effects of parameters associated with the slow current and the slower dynamical process. We find that the system presents diversity of bifurcations such as period-doubling, symmetry breaking, crises and reverse period-doubling, when the afore mentioned parameters are varied in tiny steps. The complexity of the bifurcation structures seems useful to understand how neurons encode information or how they respond to external stimuli. Furthermore, we find that the extended Hindmarsh-Rose model also presents the multistability of oscillatory and silent regimes for precise sets of its parameters. This phenomenon plays a practical role in short-term memory and appears to give an evolutionary advantage for neurons since they constitute part of multifunctional microcircuits such as central pattern generators.
The European Physical Journal Special Topics, 2016
In this work, we propose changes in the structure of a neuronal network with the intention to pro... more In this work, we propose changes in the structure of a neuronal network with the intention to provoke strong synchronization to simulate episodes of epileptic seizure. Starting with a network of Izhikevich neurons we slowly increase the number of connections in selected nodes in a controlled way, to produce (or not) hubs. We study how these structures alter the synchronization on the spike firings interval, on individual neurons as well as on mean values, as a function of the concentration of connections for random and non-random (hubs) distribution. We also analyze how the post-ictal signal varies for the different distributions. We conclude that a network with hubs is more appropriate to represent an epileptic state. BSM thanks the UNIEMP for their support. HAC thanks the FAPESP (process 2011/ 11973-4) for their support.
Nontrivial dynamics induced by a nonlinear Jaynes-Cummings Hamiltonian
Physics Letters A, 1994
... Rev. A 26 (1982), p. 676. Full Text via CrossRef. 5. V. Bu ek and I. Jex Opt. Commun. 78 (199... more ... Rev. A 26 (1982), p. 676. Full Text via CrossRef. 5. V. Bu ek and I. Jex Opt. Commun. 78 (1990), p. 425. Abstract | PDF (810 K) | View Record in Scopus | Cited By in Scopus (79). 6. Ho Trung Dung and AS Shumovsky Phys. Lett. A 160 (1991), p. 437. 7. A. Joshi and RR Puri Phys. ...
Longitudinal ultrasonic attenuation in clean type II superconductors
Solid State Communications, 1969
Abstract The attenuation of longitudinal sound in clean type II superconductors, near H c2 , has ... more Abstract The attenuation of longitudinal sound in clean type II superconductors, near H c2 , has been calculated using a non-perturbative method. It is shown that at low frequencies the attenuation rate depends strongly on the direction of propagation of the wave, and on impurity concentration.
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Papers by Hilda Cerdeira