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Kirill Kovalenko

Publications and source records attributed to Kirill Kovalenko.

7 recordsLinked to original sources
arXiv2026

Inertial synchronization of networked oscillators in arbitrary dimensions

The Kuramoto model provides a paradigmatic framework for studying synchronization of interacting oscillators, and has been generalized to arbitrary dimensions to describe swarms, flocks and multi-dimensional opinion dynamics. Yet, existing formulations neglect inertia, a key mechanism known to enhance information propagation and collective responsiveness. Here, we introduce and analyze an inertial Kuramoto model in arbitrary dimensions. We show that inertia fundamentally alters the nature of the synchronization transition, inducing a crossover from continuous to discontinuous behavior, with the onset of hysteresis depending explicitly on both inertia and dimensionality parity. Our analytical theory is supported by extensive numerical simulations. These results establish inertia as a crucial ingredient of high-dimensional collective dynamics and reveal a novel universal structure in synchronization phenomena.

nlin.AO↗
arXiv2025

For how long time evolution of chaotic or random systems can be predicted

Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications, but untreatable rigorously (mathematically). The same attitude was in the theory of strongly chaotic dynamical systems, which evolve similarly to stochastic processes. However, a natural question on dependence of the process of escape on a position of a "hole" in the state (phase) space, which was never asked in mathematical theory of open dynamical systems, opened up a new direction of research, which was dealing with finite time predictions of evolutions of such systems. It turned out, that transport of orbits in the phase space of the "most strongly chaotic" dynamical systems has three different stages. In the first stage there is a hierarchy of the first hitting probabilities, that shows which parts of the phase space the orbits of a system, which is an equilibrium state, will be more likely to visit the first. A principal (and the most important for applications) question was how the length of this interval changes with more refinement observations of the positions of the orbits in the phase space. Surprisingly, it turned out that the length of the time interval, where finite time predictions are possible, increases (rather to be shrinking), which, at the first sight, seems to be natural. However, this increase of the length of the time interval, where finite time predictions are possible, was rather slow (just linear) with respect to the growth of precision (partition of the phase space) of observations. In the present paper it is proved (by totally different technique) that this growth is actually exponential.

nlin.CD↗
arXiv2025

Equitability and explosive synchronisation in multiplex and higher-order networks

Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units. However, it is not known under which conditions equitability-induced synchronisation is the only cluster synchronisation that can occur on a particular system. Here, we reveal a natural linear independent condition such that equitability becomes necessary, and sufficient, for the existence of cluster synchronised solutions on a very general dynamical system which allows multiplex or higher-order, arbitrarily weighted interactions. Our results explain the ubiquity of explosive synchronisation, as opposed to cluster synchronisation, in multiplex and higher-order networks: equitability imposes additional constraints that must be simultaneously satisfied on the same set of nodes. Our results have significant implications for the design of complex dynamical systems of coupled dynamical units with arbitrary cluster synchronisation patterns and coupling functions.

nlin.AO↗
arXiv2023

The transition to synchronization of networked systems

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network's nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.

physics.soc-ph↗
arXiv2022

Why are there six degrees of separation in a social network?

A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultra-small world organization, whereby the graph's diameter is independent of the network size over several orders of magnitude, is still unknown. We show that the 'six degrees of separation' are the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. We show, moreover, that the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.

physics.soc-ph↗
arXiv2022

Vector Centrality in Hypergraphs

Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards network structures which go beyond a simple collection of dyadic interactions has rendered them void of performance guarantees. We here introduce a new measure of node's centrality, which is no longer a scalar value, but a vector with dimension one lower than the highest order of interaction in a hypergraph. Such a vectorial measure is linked to the eigenvector centrality for networks containing only dyadic interactions, but it has a significant added value in all other situations where interactions occur at higher-orders. In particular, it is able to unveil different roles which may be played by the same node at different orders of interactions -- information that is otherwise impossible to retrieve by single scalar measures. We demonstrate the efficacy of our measure with applications to synthetic networks and to three real world hypergraphs, and compare our results with those obtained by applying other scalar measures of centrality proposed in the literature.

physics.soc-ph↗