Topological features of spike trains in recurrent spiking neural networks that are trained to generate spatiotemporal patterns.

In this study, we focus on training recurrent spiking neural networks to generate spatiotemporal patterns in the form of closed two-dimensional trajectories. Spike trains in the trained networks are examined in terms of their dissimilarity using the Victor-Purpura distance. We apply algebraic topology methods to the matrices obtained by rank-ordering the entries of the distance matrices, specifically calculating the persistence barcodes and Betti curves.

Adaptive myelination causes slow oscillations in recurrent neural loops.

The brain is known to be plastic, i.e., capable of changing and reorganizing as it develops and accumulates experience.

Adaptation rules inducing synchronization of heterogeneous Kuramoto oscillator network with triadic couplings.

A class of adaptation functions is found for which a synchronous mode with different number of phase clusters exists in a network of phase oscillators with triadic couplings. This mode is implemented in a fairly wide range of initial conditions and the maximum number of phase clusters is four. The joint influence of coupling strength and adaptation parameters on synchronization in the network has been studied.

Bistability of operating modes and their switching in a three-machine power grid.

We consider a power grid consisting of three synchronous generators supplying a common static load, in which one of the generators is located electrically much closer to the load than the others, due to a shorter transmission line with longitudinal inductance compensation. A reduced model is derived in the form of an ensemble with a star (hub) topology without parameter interdependence. We show that stable symmetric and asymmetric synchronous modes can be realized in the grid, which differ, in particular, in the ratio of currents through the second and third power supply paths.

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.

Transient Phase Clusters in a Two-Population Network of Kuramoto Oscillators with Heterogeneous Adaptive Interaction.

Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character of adaptive couplings influences the emergence of new scenarios in the collective behavior of networks.

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.

A new scenario for Braess's paradox in power grids.

We consider several topologies of power grids and analyze how the addition of transmission lines affects their dynamics. The main example we are dealing with is a power grid that has a tree-like three-element motif at the periphery. We establish conditions where the addition of a transmission line in the motif enhances its stability or induces Braess's paradox and reduces stability of the entire grid.

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.

Noise-induced dynamical regimes in a system of globally coupled excitable units.

We study the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. Performing a numerical bifurcation analysis of the nonlocal nonlinear Fokker-Planck equation for the thermodynamic limit, we identify a complex bifurcation scenario with regions of different dynamical regimes, including collective oscillations and coexistence of states with different levels of activity. In systems of finite size, this leads to additional dynamical features, such as collective excitability of different types and noise-induced switching and bursting.

Transient circulant clusters in two-population network of Kuramoto oscillators with different rules of coupling adaptation.

We considered a network consisting of two populations of phase oscillators, the interaction of which is determined by different rules for the coupling adaptation. The introduction of various adaptation rules leads to the suppression of splay states and the emergence of each population complex non-stationary behavior called transient circulant clusters. In such states, each population contains a pair of anti-phase clusters whose size and composition slowly change over time as a result of successive transitions of oscillators between clusters.

Reduction of the collective dynamics of neural populations with realistic forms of heterogeneity.

Reduction of collective dynamics of large heterogeneous populations to low-dimensional mean-field models is an important task of modern theoretical neuroscience. Such models can be derived from microscopic equations, for example with the help of Ott-Antonsen theory. An often used assumption of the Lorentzian distribution of the unit parameters makes the reduction especially efficient.

Emergence and synchronization of a reversible core in a system of forced adaptively coupled Kuramoto oscillators.

We report on the phenomenon of the emergence of mixed dynamics in a system of two adaptively coupled phase oscillators under the action of a harmonic external force. We show that in the case of mixed dynamics, oscillations in forward and reverse time become similar, especially at some specific frequencies of the external force. We demonstrate that the mixed dynamics prevents forced synchronization of a chaotic attractor.

The third type of chaos in a system of two adaptively coupled phase oscillators.

We study a new type of attractor, the so-called reversible core, which is a mathematical image of mixed dynamics, in a strongly dissipative time-irreversible system of two adaptively coupled phase oscillators. The existence of mixed dynamics in this system was proved in our previous article [A. A.

On the intersection of a chaotic attractor and a chaotic repeller in the system of two adaptively coupled phase oscillators.

We report on the phenomenon of intersection of a chaotic attractor and a chaotic repeller in a system of two adaptively coupled phase oscillators. This is a feature of the presence of the so-called mixed dynamics, which is a new type of chaos characterized by the fundamental inseparability of conservative and dissipative behavior. The considered system is the first example of a time-irreversible system in which this type of dynamics is observed.

Hierarchical frequency clusters in adaptive networks of phase oscillators.

Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this paper, we investigate the dynamics of this system.

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.

Itinerant chimeras in an adaptive network of pulse-coupled oscillators.

In a network of pulse-coupled oscillators with adaptive coupling, we discover a dynamical regime which we call an "itinerant chimera." Similarly as in classical chimera states, the network splits into two domains, the coherent and the incoherent. The drastic difference is that the composition of the domains is volatile, i.

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.

Synchronization of chimera states in a multiplex system of phase oscillators with adaptive couplings.

We study the interaction of chimera states in multiplex two-layer systems, where each layer represents a network of interacting phase oscillators with adaptive couplings. A feature of this study is the consideration of synchronization processes for a wide range of chimeras with essentially different properties, which are achieved due to the use of different types of coupling adaptation within isolated layers. We study the effect of forced synchronization of chimera states under unidirectional action between layers.

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.

Embedding the dynamics of a single delay system into a feed-forward ring.

We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings.

Self-organized emergence of multilayer structure and chimera states in dynamical networks with adaptive couplings.

We report the phenomenon of self-organized emergence of hierarchical multilayered structures and chimera states in dynamical networks with adaptive couplings. This process is characterized by a sequential formation of subnetworks (layers) of densely coupled elements, the size of which is ordered in a hierarchical way, and which are weakly coupled between each other. We show that the hierarchical structure causes the decoupling of the subnetworks.

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.