适应与自组织系统

In this work, we propose an interdependent, multilayer network model and percolation process that matches infrastructures better than previous models by allowing some nodes to survive when their interdependent neighbors fail. We consider a…

In the Bak-Sneppen model, the lowest fitness particle and its two nearest neighbors are renewed at each temporal step with a uniform (0,1) fitness distribution. The model presents a critical value that depends on the interaction criteria…

We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative…

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…

We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the…

The model of a memristor-based oscillator with cubic nonlinearity is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria in the phase space. Numerical modeling of the dynamics is combined…

Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the M\"obius group acting on the state space $T^N$ (the $N$-fold torus). This result has been used to…

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…

The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…

We investigate the complex spatiotemporal dynamics of an ecological network with species dispersal mediated via a mean-field coupling. The local dynamics of the network are governed by the Truscott--Brindley model, which is an important…

We present a collective coordinate approach to study the collective behaviour of a finite ensemble of $N$ stochastic Kuramoto oscillators using two degrees of freedom; one describing the shape dynamics of the oscillators and one describing…

Interacting random field of probabilities links Kolmogorov law 0-1 and Bayesian probabilities observing Markov diffusion process under Yes-No actions of random impulse. These objective probabilities measure virtual probing impulses…

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the…

We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…

Network science is increasingly being developed to get new insights about behavior and properties of complex systems represented in terms of nodes and interactions. One useful approach is investigating localization properties of…

A model of the oscillatory component of interaction of inner boundaries is studied; and the features of generation of the composite structure in interim asymptotics are considered. A model of a multiscale net of inner boundaries was used to…

An important question for the practical applicability of the highly efficient traffic intersection control is about the minimal level of intelligence the vehicles need to have so as to move beyond the traffic light control. We propose an…

A plausible mechanism of self-regulation in technological chains of the kind wherein input resources are converted into common final product through sequences of processing links having uniform kinetic properties is discussed. A bottleneck…

While interdependent systems have usually been associated with increased fragility, we show that strengthening the interdependence between dynamical processes on different networks can make them more robust. By coupling the dynamics of…

A novel possibility of self-organized behaviour of stochastically driven oscillators is presented. It is shown that synchronization by L\'evy stable processes is significantly more efficient than that by oscillators with Gaussian…