适应与自组织系统

Collapses of dynamical systems into irrecoverable states are observed in ecosystems, human societies, financial systems and network infrastructures. Despite their widespread occurrence and impact, these events remain largely unpredictable.…

We analyze a large system of heterogeneous quadratic integrate-and-fire (QIF) neurons with time delayed, all-to-all synaptic coupling. The model is exactly reduced to a system of firing rate equations that is exploited to investigate the…

Computational modelling of two- and three-oscillator schemes with thermally coupled $VO_2$-switches is used to demonstrate a novel method of pattern storage and recognition in an impulse oscillator neural network (ONN) based on the…

We study the robustness of an evolving system that is driven by successive inclusions of new elements or constituents with $m$ random interactions to older ones. Each constitutive element in the model stays either active or is temporarily…

Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains…

We analyze accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations are considered: (i) the Ott-Antonsen ansatz, (ii) the…

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all…

The synchronization of self-propelled particles (SPPs) is a fascinating instance of emergent behavior in living and man-made systems, such as colonies of bacteria, flocks of birds, robot ensembles, and many others. The recent discovery of…

We present a model for the time evolution of network architectures based on dynamical systems. We show that the evolution of the existence of a connection in a network can be described as a stochastic non-markovian telegraphic signal…

Standard dynamical systems theory is centred around the coordinate-invariant asymptotic-time properties of autonomous systems. We identify three limitations of this approach. Firstly, we discuss how the traditional approach cannot take into…

We study the synchronization of Kuramoto oscillators on networks where only a fraction of them is subjected to a periodic external force. When all oscillators receive the external drive the system always synchronize with the periodic force…

The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent…

The question of the stability of unstable states of dynamical systems that do not explicitly contain a small parameter, chaos and bifurcations in them has attracted attention ever since [1-14]. This is due to the fact that this problem…

We investigate the impact of a common external system, which we call a common environment, on the Oscillator Death (OD) states of a group of Stuart-Landau oscillators. The group of oscillators yield a completely symmetric OD state when…

Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…

This study deals with the evolution of the so called 'intelligent' networks (insect society without leader, cells of an organism, brain,...) during their learning period. First we summarize briefly the Version 2 (published in French), whose…

Many coordination phenomena in Nature are grounded on a synchronisation regime. In the case of brain dynamics, such self-organised process allows the neurons of particular brain regions to behave as a whole and thus directly controlling the…

In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li1,Li2} and many other papers…

The excitable behaviour is considered as motion of a particle in a potential field in the presence of dissipation. The dynamics of the oscillator proposed in the present paper corresponds to the excitable behaviour in a potential well under…

Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…