Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Window of Chaotic Delayed Synchronization

We consider a general coupling of two chaotic dynamical systems and we obtain conditions that provide delayed synchronization. We consider four different couplings that satisfy those conditions. We define Window of Delayed Synchronization and we obtain it analytically. We use four different free chaotic dynamics in order to observe numerically the analytically predicted windows for the considered couplings.

Explosive synchronization enhanced by time-delayed coupling

This paper deals with the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees, and a time delay is included in the system. This assumption allows enhancing the explosive transition to reach a synchronous state. We provide an analytical treatment developed in a star graph, which reproduces results obtained in scale-free networks. Our findings have important implications in understanding the synchronization of complex networks since the time delay is present in most real-world complex systems due to the finite speed of the signal transmission over a distance.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

Altered Local Beta and Gamma Synchronization in Prefrontal Cortex of Mice with Redox Dysregulation or Maternal Immune Activation

Background: A developmental dysregulation of glutathione (GSH) synthesis leading to oxidative stress, when combined with environmental risk factors (viral infections) generating reactive oxygen species, can play a critical role in inducing schizophrenia phenotypes. GSH deficit induces morphological, physiological and behavioral anomalies analogous to those reported in schizophrenic patients, including disrupted parvalbumine (PV) inhibitory interneuron's integrity and neuronal synchrony (β/γ-oscillations). Methods: We assessed PV immunoreactivity (PV-IR) and local synchronization in prefrontal cortex of two mouse models: (1) mice with a genetic deficit in GSH (GCLM-/-) and (2) mice with prenatal immune activation at embryonic day17 (PolyI:C). Results: Adults from both mice models display reduced PV-IR in prefrontal cortex. In anterior cingulate (ACC) of GCLM-/-, appearance and maturation of PVI are delayed and worsened with peribubertal stress but not in adult one. This effect is reversed by treatment with the GSH precursor N-acetyl-cysteine. The power of beta and gamma oscillations are decreased in ACC of GCLM-/- while they increased in prelimbic cortex of PolyI:C mice. Conclusions: Despite reduced PV-IR in both models, alteration of the synchronization was different, indicating that the structural/functional disruption of the cortical circuitry was partly different in both models. Novel therapeutic strategies are proposed, based on interference with oxidative stress and inflammatory processes.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

Synchronization between prefrontal and posterior association cortex during human working memory

We measured coherence between the electroencephalogram at different scalp sites while human subjects performed delayed response tasks. The tasks required the retention of either verbalizable strings of characters or abstract line drawings. In both types of tasks, a significant enhancement in coherence in the θ range (4–7 Hz) was found between prefrontal and posterior electrodes during 4-s retention intervals. During 6-s perception intervals, far fewer increases in θ coherence were found. Also in other frequency bands, coherence increased; however, the patterns of enhancement made a relevance for working memory processes seem unlikely. Our results suggest that working memory involves synchronization between prefrontal and posterior association cortex by phase-locked, low frequency (4–7 Hz) brain activity.

Neural Mechanisms And Delayed Gastric Emptying Of Liquid Induced Through Acute Myocardial Infarction In Rats.

Background: In pathological situations, such as acute myocardial infarction, disorders of motility of the proximal gut can trigger symptoms like nausea and vomiting. Acute myocardial infarction delays gastric emptying (GE) of liquid in rats. Objective: Investigate the involvement of the vagus nerve, α 1-adrenoceptors, central nervous system GABAB receptors and also participation of paraventricular nucleus (PVN) of the hypothalamus in GE and gastric compliance (GC) in infarcted rats. Methods: Wistar rats, N = 8-15 in each group, were divided as INF group and sham (SH) group and subdivided. The infarction was performed through ligation of the left anterior descending coronary artery. GC was estimated with pressure-volume curves. Vagotomy was performed by sectioning the dorsal and ventral branches. To verify the action of GABAB receptors, baclofen was injected via icv (intracerebroventricular). Intravenous prazosin was used to produce chemical sympathectomy. The lesion in the PVN of the hypothalamus was performed using a 1mA/10s electrical current and GE was determined by measuring the percentage of gastric retention (% GR) of a saline meal. Results: No significant differences were observed regarding GC between groups; vagotomy significantly reduced % GR in INF group; icv treatment with baclofen significantly reduced %GR. GABAB receptors were not conclusively involved in delaying GE; intravenous treatment with prazosin significantly reduced GR% in INF group. PVN lesion abolished the effect of myocardial infarction on GE. Conclusion: Gastric emptying of liquids induced through acute myocardial infarction in rats showed the involvement of the vagus nerve, alpha1- adrenergic receptors and PVN.Fundamento: Distúrbios da motilidade do intestino proximal no infarto agudo do miocárdio podem desencadear sintomas digestivos como náuseas e vômitos. O infarto do miocárdio ocasiona retardo do esvaziamento gástrico (EG) de líquido em ratos. Objetivo: Investigar se existe a influência do nervo vago (VGX), adrenoreceptores α-1, receptores GABAB do sistema nervoso central e participação do núcleo paraventricular (NPV) do hipotálamo no esvaziamento gástrico (EG) e complacência gástrica (CG) em ratos infartados. Métodos: Ratos Wistar (n = 8-15) foram divididos em: grupo infarto (INF), sham (SH) e subdivididos. O infarto foi realizado por ligadura da artéria coronária descendente anterior. A complacência gástrica foi estimada com curvas pressão-volume. Realizada vagotomia por secção dos ramos dorsal e ventral. Para verificar a ação dos receptores GABAB foi injetado baclofeno por via intra ventrículo-cerebral. Simpatectomia química foi realizada com prazosina intravenosa (iv), e na lesão do núcleo paraventricular do hipotálamo foi utilizada corrente elétrica de 1mA/10s, com esvaziamento gástrico determinado por medição da retenção gástrica (% RG) de uma refeição salina. Resultados: Não houve diferença significativa na CG. A vagotomia (VGX) reduziu significativamente a %RG; no grupo INF, o tratamento intra ventrículo-cerebral (ivc) com baclofeno reduziu significativamente a % RG; não houve conclusivamente envolvimento dos receptores GABAB em retardar o EG; o tratamento intravenoso com prazosina reduziu significativamente a %RG no grupo INF. A lesão do NPV aboliu o efeito do infarto do miocárdio no EG. Conclusão: O nervo vago, receptores α-adrenérgicos e núcleo paraventricular estão envolvidos no retardo do esvaziamento gástrico no infarto agudo do miocárdio em ratos.

Explosive Synchronization With Partial Degree-frequency Correlation.

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of their corresponding vertices exhibit so-called explosive synchronization behavior, which is now under intensive investigation. Here we study and discuss explosive synchronization in a situation that has not yet been considered, namely when only a part, typically a small part, of the vertices is subjected to a degree-frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform a mean-field analysis and our conclusions were corroborated by exhaustive numerical experiments for synthetic networks and also for the undirected and unweighed version of a typical benchmark biological network, namely the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed.

Multistable behavior above synchronization in a locally coupled Kuramoto model

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that the solutions possess different characteristics, depending on the section of the boundary of the SR where they appear. We study the birth of these solutions and how they evolve when the coupling strength increases, and determine the diagram of solutions in phase space.

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbor coupling. Upon analyzing the behavior of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.

Diffusive Synchronization of Hyperchaotic Lorenz Systems

The synchronizing properties of two diffusively coupled hyperchaotic Lorenz 4D systems are investigated by calculating the transverse Lyapunov exponents and by observing the phase space trajectories near the synchronization hyperplane. The effect of parameter mismatch is also observed. A simple electrical circuit described by the Lorenz 4D equations is proposed. Some results from laboratory experiments with two coupled circuits are presented. Copyright (C) 2009 Ruy Barboza.

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels

Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal. Copyright (C) 2009 Marcio Eisencraft et al.