arXiv subjects

C. G. Antonopoulos

Publications and source records attributed to C. G. Antonopoulos.

4 recordsLinked to original sources

arXiv2022

Energy-recurrence Breakdown and Chaos in Disordered Fermi-Pasta-Ulam-Tsingou Lattices

In this paper, we consider the classic Fermi-Pasta-Ulam-Tsingou system as a model of interacting particles connected by harmonic springs with a quadratic nonlinear term (first system) and a set of second-order ordinary differential equations with variability (second system) that resembles Hamilton's equations of motion of the Fermi-Pasta-Ulam-Tsingou system. In the absence of variability, the second system becomes Hamilton's equations of motion of the Fermi-Pasta-Ulam-Tsingou system (first system). Variability is introduced to Hamilton's equations of motion of the Fermi-Pasta-Ulam-Tsingou system to take into account inherent variations (for example, due to manufacturing processes), giving rise to heterogeneity in its parameters. We demonstrate that a percentage of variability smaller than a threshold can break the well-known energy recurrence phenomenon and induce localization in the energy normal-mode space. However, percentage of variability larger than the threshold may make the trajectories of the second system blow up in finite time. Using a multiple-scale expansion, we derive analytically a two normal-mode approximation that explains the mechanism for energy localization and blow up in the second system. We also investigate the chaotic behavior of the two systems as the percentage of variability is increased, utilising the maximum Lyapunov exponent and Smaller Alignment Index. Our analysis shows that when there is almost energy localization in the second system, it is more probable to observe chaos, as the number of particles increases.

math.DS↗

arXiv2021

Spatiotemporal characteristics in systems of diffusively coupled excitable slow-fast FitzHugh-Rinzel dynamical neurons

In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the formation of spatiotemporal patterns. We focus on local, nonlinear excitations and diverse neural responses in an excitable 1- and 2-dimensional configuration of diffusively coupled FitzHugh-Rinzel neurons. The study of the emerging spatiotemporal patterns is essential in understanding the working mechanism in different brain areas. We derive analytically the coefficients of the amplitude equations in the vicinity of Hopf bifurcations and characterize various patterns, including spirals exhibiting complex geometric substructures. Further, we derive analytically the condition for the development of antispirals in the neighborhood of the bifurcation point. The emergence of broken target waves can be observed to form spiral-like profiles. The spatial dynamics of the excitable system exhibits 2- and multi-arm spirals for small diffusive couplings. Our results reveal a multitude of neural excitabilities and possible conditions for the emergence of spiral-wave formation. Finally, we show that the coupled excitable systems with different firing characteristics, participate in a collective behavior that may contribute significantly to irregular neural dynamics.

nlin.CD↗

arXiv2020

Influence of autapses on synchronisation in neural networks with chemical synapses

A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronisation. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behaviour. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neural networks consisting of both excitatory and inhibitory neurons, we uncover that synchronous behaviour depends on their synapse type. Our results provide evidence on the synchronous and desynchronous activities that emerge in random neural networks with chemical, inhibitory and excitatory synapses where neurons are equipped with autapses.

q-bio.NC↗

arXiv2019

Bistable firing pattern in a neural network model

Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronisation mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronisation in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronisation originating from a pattern of desynchronised spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronisation, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronisation by applying a small-amplitude external current on less than 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behaviour, but more importantly, it can be used as a means to reduce abnormal synchronisation and thus, control or treat effectively epileptic seizures.

physics.bio-ph↗