Related papers: Rhythms of the nervous system: mathematical themes…
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…
Fluctuations in the abundance of molecules in the living cell may affect its growth and well being. For regulatory molecules (e.g., signaling proteins or transcription factors), fluctuations in their expression can affect the levels of…
We have analysed the many facets of Consciousness into two distinct categories. First: the organisational state of the neural networks at any one time, which determines whether a person is conscious - awake, or unconscious - asleep. Second:…
The net of N ``physical'' neurons is considered as a dynamical system. These neurons form a complete graph. The state of any neuron is its electric potential. The potential linearly increases until reaches its maximal value. Then it falls…
We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…
Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…
When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available…
Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…
We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and…
The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…
This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…
In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media…
Noisy fluctuations are ubiquitous in complex systems. They play a crucial or delicate role in the dynamical evolution of gene regulation, signal transduction, biochemical reactions, among other systems. Therefore, it is essential to…
Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
Experimental fMRI studies have shown that spontaneous brain activity i.e. in the absence of any external input, exhibit complex spatial and temporal patterns of co-activity between segregated brain regions. These so-called large-scale…