Related papers: Chaos in Small-World Networks
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
Since its recent introduction, the small-world effect has been identified in several important real-world systems. Frequently, it is a consequence of the existence of a few long-range connections, which dominate the original regular…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
We investigate temporal coherence and spatial synchronization on small-world networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence on two types of time-delayed coupling: $\{x_j(t-\tau)-x_i (t)\}$ and…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of…
We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of…
We consider critical phenomena on heterogeneous small-world networks having a scale-free character but also arbitrary short-loops. After deriving the self-consistent equation for the order parameter and the critical surface, we prove that…
We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
We study the constructive role of noises in a Lorenz system with functional delay. The effect of delay can change the dynamics of the system to a chaotic one from its steady state. Induced synchronization with white and colored (red and…
We study chaotic systems with multiple time delays that range over several orders of magnitude. We show that the spectrum of Lyapunov exponents (LE) in such systems possesses a hierarchical structure, with different parts scaling with the…
The observed long-range spatiotemporal correlations of real world dynamical systems is governed by quantumlike mechanics with inherent non-local connections. In summary, microscopic scale local fluctuations form a unified self-organized…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the…
Resilience of the most important properties of stochastic and regular (deterministic) small-world interconnection networks is studied. It is shown that in the broad range of values of the fraction of faulty nodes the networks under…
Recent research has shown the deep impact of the dynamics of human interactions (or temporal social networks) on the spreading of information, opinion formation, etc. In general, the bursty nature of human interactions lowers the…