Stochastic and deterministic dynamics in networks with excitable nodes.
Chaos
; 33(2): 023134, 2023 Feb.
Article
em En
| MEDLINE
| ID: mdl-36859228
ABSTRACT
Networks of excitable systems provide a flexible and tractable model for various phenomena in biology, social sciences, and physics. A large class of such models undergo a continuous phase transition as the excitability of the nodes is increased. However, models of excitability that result in this continuous phase transition are based implicitly on the assumption that the probability that a node gets excited, its transfer function, is linear for small inputs. In this paper, we consider the effect of cooperative excitations, and more generally the case of a nonlinear transfer function, on the collective dynamics of networks of excitable systems. We find that the introduction of any amount of nonlinearity changes qualitatively the dynamical properties of the system, inducing a discontinuous phase transition and hysteresis. We develop a mean-field theory that allows us to understand the features of the dynamics with a one-dimensional map. We also study theoretically and numerically finite-size effects by examining the fate of initial conditions where only one node is excited in large but finite networks. Our results show that nonlinear transfer functions result in a rich effective phase diagram for finite networks, and that one should be careful when interpreting predictions of models that assume noncooperative excitations.
Texto completo:
1
Base de dados:
MEDLINE
Tipo de estudo:
Prognostic_studies
Idioma:
En
Revista:
Chaos
Assunto da revista:
CIENCIA
Ano de publicação:
2023
Tipo de documento:
Article
País de afiliação:
Irã