Internal dynamics of recurrent neural networks trained to generate complex spatiotemporal patterns.

How complex patterns generated by neural systems are represented in individual neuronal activity is an essential problem in computational neuroscience as well as machine learning communities. Here, based on recurrent neural networks in the form of feedback reservoir computers, we show microscopic features resulting in generating spatiotemporal patterns including multicluster and chimera states. We show the effect of individual neural trajectories as well as whole-network activity distributions on exhibiting particular regimes.

Multitask computation through dynamics in recurrent spiking neural networks.

In this work, inspired by cognitive neuroscience experiments, we propose recurrent spiking neural networks trained to perform multiple target tasks. These models are designed by considering neurocognitive activity as computational processes through dynamics. Trained by input-output examples, these spiking neural networks are reverse engineered to find the dynamic mechanisms that are fundamental to their performance.

Disordered quenching in arrays of coupled Bautin oscillators.

In this work, we study the phenomenon of disordered quenching in arrays of coupled Bautin oscillators, which are the normal form for bifurcation in the vicinity of the equilibrium point when the first Lyapunov coefficient vanishes and the second one is nonzero. For particular parameter values, the Bautin oscillator is in a bistable regime with two attractors-the equilibrium and the limit cycle-whose basins are separated by the unstable limit cycle. We consider arrays of coupled Bautin oscillators and study how they become quenched with increasing coupling strength.

Collective dynamics of rate neurons for supervised learning in a reservoir computing system.

In this paper, we study collective dynamics of the network of rate neurons which constitute a central element of a reservoir computing system. The main objective of the paper is to identify the dynamic behaviors inside the reservoir underlying the performance of basic machine learning tasks, such as generating patterns with specified characteristics. We build a reservoir computing system which includes a reservoir-a network of interacting rate neurons-and an output element that generates a target signal.

Hierarchical transitions in multiplex adaptive networks of oscillatory units.

In this work, we consider two-layer multiplex networks of coupled Stuart-Landau oscillators. The first layer contains oscillators with amplitude heterogeneity and all-to-all adaptive links, while the second layer contains identical oscillators all-to-all coupled by links with constant weights. The links between different layers are adaptive and organized in a one-to-one manner.

Transient chaos in the Lorenz-type map with periodic forcing.

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates.

Mean-field dynamics of a population of stochastic map neurons.

We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series.

Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons.

We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network exhibits a sequence of transient clustering which relates to a traffic in the hypernetwork in the form of a random walk. Receiving inputs the system is able to generate reproducible sequences corresponding to stimulus-specific paths in the hypernetwork.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos.

Basin stability for burst synchronization in small-world networks of chaotic slow-fast oscillators.

The impact of connectivity and individual dynamics on the basin stability of the burst synchronization regime in small-world networks consisting of chaotic slow-fast oscillators is studied. It is shown that there are rewiring probabilities corresponding to the largest basin stabilities, which uncovers a reason for finding small-world topologies in real neuronal networks. The impact of coupling density and strength as well as the nodal parameters of relaxation or excitability are studied.

Modular networks with delayed coupling: synchronization and frequency control.

We study the collective dynamics of modular networks consisting of map-based neurons which generate irregular spike sequences. Three types of intramodule topology are considered: a random Erdös-Rényi network, a small-world Watts-Strogatz network, and a scale-free Barabási-Albert network. The interaction between the neurons of different modules is organized by relatively sparse connections with time delay.

Emergence of antiphase bursting in two populations of randomly spiking elements.

Animal locomotion activity relies on the generation and control of coordinated periodic actions in a central pattern generator (CPG). A core element of many CPGs responsible for the rhythm generation is a pair of reciprocally coupled neuron populations. Recent interest in the development of highly reduced models of CPG networks is motivated by utilization of CPG models in applications for biomimetic robotics.

Dynamic boundary crisis in the Lorenz-type map.

Effects of the slowly varying control parameters on bifurcations of the equilibria and limit cycles have been previously studied in detail. In this paper, the concept of dynamic bifurcations is extended to chaotic phenomena. We consider this problem for a Lorenz-type map.