适应与自组织系统

Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with…

Coupling among neural rhythms is one of the most important mechanisms at the basis of cognitive processes in the brain. In this study we consider a neural mass model, rigorously obtained from the microscopic dynamics of an inhibitory…

We consider anti-phase synchronization of coupled oscillators using the Stuart-Landau model and explore its relative infrequency in occurrence compared to in-phase synchronization. We report effective limits in number of oscillators which…

One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…

Initially, the logistic map became popular as a simplified model for population growth. In spite of its apparent simplicity, as the population growth-rate is increased the map exhibits a broad range of dynamics, which include bifurcation…

Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here we attempt to describe it using an AC threshold…

An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge,…

For any network of identical Kuramoto oscillators with identical positive coupling, there is a critical connectivity above which the system is guaranteed to converge to the in-phase synchronous state, for almost all initial conditions. But…

We investigate how locomotory behavior is generated in the brain focusing on the paradigmatic connectome of nematode Caenorhabditis elegans (C. elegans) and on neuronal activity patterns that control forward locomotion. We map the neuronal…

Identifying key players in a set of coupled individual systems is a fundamental problem in network theory. Its origin can be traced back to social sciences and led to ranking algorithms based on graph theoretic centralities. Coupled…

Chimera state refers to coexistence of coherent and non-coherent phases in identically coupled dynamical units found in various complex dynamical systems. Identification of Chimera, on one hand is essential due to its applicability in…

We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic…

We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems…

We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the…

The spread of perturbative signals in complex networks is governed by the combined effect of the network topology and its intrinsic nonlinear dynamics. Recently, the resulting spreading patterns have been analyzed and predicted, shown to…

Starting from a particle model we derive a macroscopic aggregation-diffusion equation for the evolution of slime mold under the assumption of propagation of chaos in the large particle limit. We analyze properties of the macroscopic model…

Chimera states in one-dimensional nonlocally coupled phase oscillators are mostly assumed to be stationary, but breathing chimeras can occasionally appear, branching from the stationary chimeras via Hopf bifurcation. In this paper, we…

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…

The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…

We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…