Related papers: Excitable behaviors
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…
Models of simple excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This subject is a topic of practical relevance to diverse fields, ranging from neuroscience to…
Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked…
This paper suggests a statistical framework for describing the relations between the physical and conceptual entities of a brain-like model. Features and concept instances are put into context, where the paper suggests that features may be…
This short article is devoted to the dynamics of controlled (and, therefore, open) systems. The internal forces, which appear only in the presence of external free controls and depend explicitely on them, are considered. Such interactive…
We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us…
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
The paper proposes two dynamical systems based on the generalized Lotka-Volterra model of three excitable elements interacting through excitatory couplings. It is shown that for some values of the coupling parameters in the phase space of…
The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects…
A naive model of many networked logistic maps with an excitation type coupling [Neural Networks, vol. 20, 102--108 (2007)], which is an extension of other low dimensional models, has been recently proposed to mimic the waking-sleeping…
In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…
A feature of the brains of intelligent animals is the ability to learn to respond to an ensemble of active neuronal inputs with a behaviorally appropriate ensemble of active neuronal outputs. Previously, a hypothesis was proposed on how…
Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well…
Many extended chemical and biological systems self-organise into complex patterns that drive the medium behaviour in a non-linear fashion. An important class of such systems are excitable media, including neural and cardiac tissues. In…
We propose a means to relate properties of an interconnected system to its separate component systems in the presence of cascade-like phenomena. Building on a theory of interconnection reminiscent of the behavioral approach to systems…
The chapter presents some new approaches to describing the collective behavior of complex systems of mathematical biology based on the evolution equations of observables such as open systems. This representation of kinetic evolution has…
Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of…
Performance of a sensory-neural network developed for diagnosing of diseases is described. Information about patient's condition is provided by answers to the questionnaire. Questions correspond to sensors generating signals when patients…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in…