相关论文: Critical Kauffman networks under deterministic asy…
The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between…
We investigate the stability of synchronization in networks of dynamical systems with strongly delayed connections. We obtain strict conditions for synchronization of periodic and equilibrium solutions. In particular, we show the existence…
The impact of finite cycles on the phantom modulus in an otherwise perfect network is computed exactly. It is shown that pending cycles reduce the phantom modulus of the network by $kT/V$ independent of junction functionality. The…
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear…
An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…
We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
We study two types of simple Boolean networks, namely two loops with a cross-link and one loop with an additional internal link. Such networks occur as relevant components of critical K=2 Kauffman networks. We determine mostly analytically…
Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can behave unexpectedly when the signal between the vertices are time delayed. It has been shown for a very…
Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the…
The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random…
We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two…
We consider a one dimensional Euclidean network which is grown using a preferential attachment. Here the $j$th incoming node gets attached to the $i$th existing node with the probability $\Pi_i \propto k_i {{l}}_{ij}^\alpha$, where…
Online advertising platforms use automated auctions to connect advertisers with potential customers, requiring effective bidding strategies to maximize profits. Accurate ad impact estimation requires considering three key factors: delayed…
We investigate the influence of time-delayed coupling in a ring network of non-locally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. We…
We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we…
In this study, we construct such systems with the Kuramoto model of globally coupled oscillators with time-delayed positive and negative couplings to explore the impact of coupling time delays in the collective frequency of synchronized…