Related papers: Nonlinear Observer Design and Synchronization Anal…
The paper addresses the problem of parameter estimation (or identification) in dynamical networks composed of an arbitrary number of FitzHugh-Nagumo neuron models with diffusive couplings between each other. It is assumed that only the…
This work delves into studying the synchronization in two realistic neuron models using Hodgkin-Huxley dynamics. Unlike simplistic point-like models, excitatory synapses are here randomly distributed along the dendrites, introducing strong…
We discuss the synchronization of coupled neurons which are modelled as FitzHugh-Nagumo systems. As smallest entity in a larger network, we focus on two diffusively coupled subsystems, which can be interpreted as two mutually interacting…
Hysteresis is a ubiquitous phenomenon in science and engineering; its modeling and identification are crucial for understanding and optimizing the behavior of various systems. We develop an ordinary differential equation-based recurrent…
It is well known that Electroencephalography(EEG) and the respective evoked potentials have deep implications corresponding to specific cognitive tasks and in the diagnosis of several diseases such as epilepsy and schizophrenia. Some recent…
We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
Neural oscillations are electrical activities of the brain measurable at different frequencies. This paper studies the interaction between the fast and slow processes in the brain. We recorded signals intracranially from the simple Wistar…
We study the nonlinear dynamics of two delay-coupled neural systems each modelled by excitable dynamics of FitzHugh-Nagumo type and demonstrate that bistability between the stable fixed point and limit cycle oscillations occurs for…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Neural Operators (NOs) are a powerful deep learning framework designed to learn the solution operator that arise from partial differential equations. This study investigates NOs ability to capture the stiff spatio-temporal dynamics of the…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times $\tau$ near but below the repetitive firing critical current, $\tau \simeq C (I_c-I)^{-\Delta}$. For both the…
The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive…
Parameter estimation in multidimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, the membrane potential evolution in…
This work is devoted to the problem of synchronization of two Morris-Lecar neuron models. The Morris-Lecar model is a second-order system of differential equations, which describes an uneasy relationship between the membrane potential and…
Constructing electronic models of neurons has several applications including reproducing dynamics of biological neurons and their networks and neuroprosthetics. In the brain, most neurons themselves are in a non-oscillatory mode, and brain…
While phase oscillators are often used to model neuronal populations, in contrast to the Kuramoto paradigm, strong interactions between brain areas can be associated with loss of synchrony. Using networks of coupled oscillators described by…
The FitzHugh-Nagumo equation, originally conceived in neuroscience during the 1960s, became a key model providing a simplified view of excitable neuron cell behavior. Its applicability, however, extends beyond neuroscience into fields like…
We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is…