Related papers: Criticality and Chaos in Systems of Communities
We introduce a simple dynamical model of two interacting communities whose elements are subject to stochastic discrete-time updates governed by only bilinear interactions. When the intra- and inter-couplings are cooperative, the two…
The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents…
Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…
We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak…
We introduce a ``spatial'' Lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow systems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase…
Chaos in both dissipative systems and conservative systems is investigated on the approach of renormalization group. It is found that the chaos is regarded as the critical phenomenon of equilibrium statistics in phase space. The two…
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
We study opinion dynamics on networks with a nontrivial community structure, assuming individuals can update their binary opinion as the result of the interactions with an external influence with strength $h\in [0,1]$ and with other…
The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…
Weakly perturbed integrable many-body systems are typically chaotic, and thermal at late times. However, there are distinct relationships between the timescales for thermalization and chaos. The typical relationship is confined chaos: when…
Fluids cooled to the liquid-vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite the rich phenomenology of this critical point, there is not currently an explanation of the…
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…
Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and…