Related papers: Failure-recovery model with competition between fa…
There is empirical evidence from a range of disciplines that as the connectivity of a network increases, we observe an increase in the average fitness of the system. But at the same time, there is an increase in the proportion of…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of…
In the framework of the evolutionary dynamics of the Prisoner's Dilemma game on complex networks, we investigate the possibility that the average level of cooperation shows hysteresis under quasi-static variations of a model parameter (the…
Systems that comprise many interacting dynamical networks, such as the human body with its biological networks or the global economic network consisting of regional clusters, often exhibit complicated collective dynamics. To understand the…
We briefly introduce hysteresis in spatially extended systems and the dynamic phase transition observed as the frequency of the oscillating field increases beyond a critical value. Hysteresis and the decay of metastable phases are closely…
A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others.…
Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently,…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
We present a simple two-dimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law…
The modeling of cascading failure in power systems is difficult because of the many different mechanisms involved; no single model captures all of these mechanisms. Understanding the relative importance of these different mechanisms is an…
Human achievements are often preceded by repeated attempts that initially fail, yet little is known about the mechanisms governing the dynamics of failure. Here, building on the rich literature on innovation, human dynamics and learning, we…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
Networked systems are susceptible to cascading failures, where the failure of an initial set of nodes propagates through the network, often leading to system-wide failures. In this work, we propose a multiplex flow network model to study…
Existing models for the analysis of concurrent processes tend to focus on fail-stop failures, where processes are either working or permanently stopped, and their state (working/stopped) is known. In fact, systems are often affected by grey…
We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles…
Many complex systems, including networks, are not static but can display strong fluctuations at various time scales. Characterizing the dynamics in complex networks is thus of the utmost importance in the understanding of these networks and…