Related papers: Complexity vs stability in small-world networks
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and…
The changing topology of a network is driven by the need to maintain or optimize network function. As this function is often related to moving quantities such as traffic, information, etc. efficiently through the network the structure of…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…
Complex systems contain a lot of individuals and some interactions between them. The structure of interactions can be modeled to be a network: nodes represent individuals and links to be interaction between two individuals. This paper tries…
Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
The Lotka-Volterra system is a set of ordinary differential equations describing growth of interacting ecological species. This model has gained renewed interest in the context of random interaction networks. One of the debated questions is…
From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy - affect their…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is…
Biological networks of interacting agents exhibit similar topological properties for a wide range of scales, from cellular to ecological levels, suggesting the existence of a common evolutionary origin. A general evolutionary mechanism…
A nonlinear small-world network model has been presented to investigate the effect of nonlinear interaction and time delay on the dynamic properties of small-world networks. Both numerical simulations and analytical analysis for networks…
Many complex networks display remarkable resilience under external perturbations, internal failures and environmental changes, yet they can swiftly deteriorate into dysfunction upon the removal of a few keystone nodes. Discovering theories…
After a failure or attack the structure of a complex network changes due to node removal. Here, we show that the degree distribution of the distorted network, under any node disturbances, can be easily computed through a simple formula.…
The basic laws of physics are simple, so why is the world complex? The theory of self-organized criticality posits that complex behavior in nature emerges from the dynamics of extended, dissipative systems that evolve through a sequence of…