Detection of nonstationary transition to synchronized states of a neural network using recurrence analyses

Abstract

We study the stability of asymptotic states displayed by a complex neural network. We focus on the loss of stability of a stationary state of networks using recurrence quantifiers as tools to diagnose local and global stabilities as well as the multistability of a coupled neural network. Numerical simulations of a neural network composed of 1024 neurons in a small-world connection scheme are performed using the model of Braun et al. [Int. J. Bifurcation Chaos 08, 881 (1998)IJBEE40218-127410.1142/S0218127498000681], which is a modified model from the Hodgkin-Huxley model [J. Phys. 117, 500 (1952)]. To validate the analyses, the results are compared with those produced by Kuramoto's order parameter [Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin Heidelberg, 1984)]. We show that recurrence tools making use of just integrated signals provided by the networks, such as local field potential (LFP) (LFP signals) or mean field values bring new results on the understanding of neural behavior occurring before the synchronization states. In particular we show the occurrence of different stationary and nonstationarity asymptotic states.

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

“…Regarding complex networks, it is known that this kind of system can show emergent behavior, where the global behavior observed is richer than the sum of the individual element behaviors. In this way, the existence of non-monotonic transitions to synchronization as a function of coupling strength in neural networks [26][27][28][29][30], where non-stationary states can be noticed, has been reported in the literature. In some cases, in the transition region, on-off intermittency in the two states has been observed, where the network displays the existence of two locally stable states but globally unstable ones [18,26], as defined in [31].…”

“…In this way, the existence of non-monotonic transitions to synchronization as a function of coupling strength in neural networks [26][27][28][29][30], where non-stationary states can be noticed, has been reported in the literature. In some cases, in the transition region, on-off intermittency in the two states has been observed, where the network displays the existence of two locally stable states but globally unstable ones [18,26], as defined in [31]. In [9], the dynamical properties regarding synchronization and transition characteristics are studied as a function of the connection architecture, with both small-world and random topologies being considered.…”

Suppression of Phase Synchronization in Scale-Free Neural Networks Using External Pulsed Current Protocols

“…It was shown that the scale-free network displays a non-monotonic evolution of the phase synchronization as the coupling between neurons increases. A similar scenario has been observed in small-world networks, which is called "anomalous phase synchronization" [30,31,55], since the traditional behavior should monotonically transition to PS [33]. Especially, Parkinson's disease and some episodes of seizure behavior generated by epilepsy may be associated to anomalous synchronization.…”

“…For the interval of coupling strength 0.002 < ε < 0.007, the network exhibited a local maximum of phase synchronization (ε ≈ 0.004). This behavior was also observed in small-world network [30,31,51], which characterized a non-monotonic evolution of the synchronization level as a function of the coupling that could be understood as an abnormal synchronization since PS occurred for a coupling ε < ε * . In this way, it is known that several brain disorders, such as Parkinson's disease and autism, are related to abnormal neuronal synchronization [6][7][8][9], thus it is expected that the application of synchronization suppression methods may be useful to vanish the anomalous synchronization, as observed in Figure 2.…”

“…It is observed in the literature that a neural network under a small-world topology can display abnormal phase synchronization for weak coupling regime since the phase synchronization regime in this region is characterized by a non-monotonic evolution of synchronization levels as a function of the coupling between neurons [29][30][31]. In fact, this kind of behavior has also been observed in non-identical coupled Rösller oscillators [32].…”