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Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We…
We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…
In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…
We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous…
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…
Noise-induced phenomena in high-dimensional dynamical systems were investigated from a random dynamical systems point of view. In a class of generalized H\'enon maps, which are randomly perturbed delayed logistic maps, with monotonically…
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…
I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
In Bohmian mechanics, the nodes of the wave function play an important role in the generation of chaos. However, so far, most of the attention has been on moving nodes; little is known about the possibility of chaos in the case of…
In neural information processing, an input modulates neural dynamics to generate a desired output. To unravel the dynamics and underlying neural connectivity enabling such input-output association, we proposed an exactly soluble…
Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and…
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…
Experimental records of active bundle motility are used to demonstrate the presence of a low-dimensional chaotic attractor in hair cell dynamics. Dimensionality tests from dynamic systems theory are applied to estimate the number of…