The role of topology in the response of networks of excitable units driven by noise

BALENZUELA, PABLO; JORDI GARCIA OJALVO

Buenos Aires

Workshop; Workshop on Dynamic Networks (WDN?13); 2013

Facultad de Ingenieria, Universidad de Buenos Aires

In this work we analyze the collective behavior of excitable units driven by noise and coupled with different network´s topologies in three different dynamical regimes. An excitable element provides a nonlinear response under any given stimulus. It can be thought basically as a threshold device: if the stimulus is above the threshold, the unit responds, otherwise, it remains silent. This reponse is usually invariant under changes in the stimulus intensity. The best example of this behavior is the action potential (or spike) of a neuron. When they are coupled in networks, the interplay between individual dynamics and underlying topology gives raise to the emergence of collective properties, such as synchronization or coherent spiking response. In the last years the synchronization of coupled chaotic oscillator and their dependence with the underlying network topology was extensively studied. It has been found that strongly heterogeneous networks (like scale free networks) synchronize worst than homogeneous ones, a phenomenon known as a the paradox of heterogeneity. However, if the links of heterogeneus networks are weighted with their betweeness, the synchronization improves notoriously. An interesting behavior of excitable elements driven by noise is the phenomenon known as "coherence resonance", which happen when neurons respond in a quasi-periodic (coherent) way for an intermediate amount of noise. In networks of excitable units, it has been found that the degree of coherence is better than in individual neurons. It means that many neurons, driven by a purely stochastic stimulus, spike more regularly than an individual neuron driven by the same stimulus. This collective behavior, known as Array Enhanced Coherence Resonance (AECR) can be achieved only if there exist a balance between the degree of synchronization of the units of the networks and its coherente behavior. In order to analyze the emergence of non-trivial collective properties related to the balance of coherence response and synchronization, we study the behavior of networks of excitable units coupled with different topologies of connections: Unweighted and Weighted Scale Free Networks (UWSFN and WSFN), Regular Networks (RN) and Random (ER) Networks in three different dynamical regimes: subthreshold, spike driven and noise driven. The results shown in this work suggest than WSFN display an optimal balance between sinchronization and coherence behavior given by the link´s weighting procedure, which reduces the heterogeinity in the node´s dynamics, improving the global response of the system.