Related papers: Heterogeneous excitable systems exhibit Griffiths …
A R\"ossler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absence of the perturbation the system is assumed to possess two…
We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of…
Many biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability. In balanced networks, strong excitatory synaptic inputs are canceled by strong inhibitory inputs…
We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment,…
The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or "in the other phase". It is known that, in one dimension, these rare regions can cause the d.c.…
The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system…
Phase transitions constitute fundamental mechanisms underlying abrupt or qualitative changes in the collective dynamics of interacting units across a wide range of natural and engineered systems. In dynamical networks, such transitions lead…
Phase transitions (PTs) are generally classified into second-order and first-order transitions, each exhibiting different intrinsic properties. For instance, a first-order transition exhibits latent heat and hysteresis when a control…
Synchronization is an important collective phenomenon in interacting oscillatory agents. Many functional features of the brain are related to synchronization of neurons. The type of synchronization transition that may occur (explosive vs.…
A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics…
We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…
Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last…
Recent studies have shown that novel collective behaviors emerge in complex systems due to the presence of higher-order interactions. However, how the collective behavior of a system is influenced by the microscopic organization of its…
We study the phase transitions in the simplicial Ising model on hypergraphs, in which the energy within each hyperedge (group) is lowered only when all the member spins are unanimously aligned. The Hamiltonian of the model is equivalent to…
A potential phase transition between a normal ground state and a photon-condensed ground state in many-dipole light-matter systems is a topic of considerable controversy, exasperated by conflicting no-go and counter no-go theorems and often…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
The Susceptible-Infected-Susceptible (SIS) model is one of the simplest memoryless system for describing information/epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched…
We use the pair heterogeneous mean-field (PHMF) approximation for an asynchronous version of the susceptible-infected-removed (SIR) model to estimate the epidemic thresholds on complex quenched networks. Our results indicate an improvement…
We study the phase fluctuations in the normal state of generic two-dimensional superconducting systems with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging,…