Related papers: Hopf-type neurons increase input-sensitivity by fo…
The population dynamics in a modified Leslie-Gower model with an additive Allee effect are highly sensitive to both parameters and initial population densities, leading to outcomes ranging from coextinction to sustained multistable steady…
Recently, it has been shown that properties of excitable media stirred by two-dimensional chaotic flows can be properly studied in a one-dimensional framework \cite{excitablePRL,excitablePRE}, describing the transverse profile of the…
It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift…
Oscillations represent a ubiquitous phenomenon in biological systems. The conventional models of biological periodic oscillations are usually proposed as interconnecting transcriptional feedback loops. Some specific proteins function as…
Theoretical investigations of dynamical behavior in optical parametric oscillators (OPO) have generally assumed that the cavity detunings of the interacting fields are controllable parameters. However, OPOs are known to experience mode…
Over the past two centuries, the frequency of word usage in major Western languages has exhibited small amplitude regular cycles, superimposed on larger background trends. We show that these cycles of word usage organize into semantically…
Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference:…
In this paper, by incorporating the general delay to the reaction term in the memory-based diffusive system, we propose a diffusive system with memory delay and general delay (e.g., digestion, gestation, hunting, migration and maturation…
The olfactory system is constantly solving pattern-recognition problems by the creation of a large space to codify odour representations and optimizing their distribution within it. A model of the Olfactory Bulb was developed by Z. Li and…
We argue that all building blocks of transformer models can be expressed with a single concept: combinatorial Hopf algebra. Transformer learning emerges as a result of the subtle interplay between the algebraic and coalgebraic operations of…
This paper proposes a neuronal circuitry layout and synaptic plasticity principles that allow the (pyramidal) neuron to act as a "combinatorial switch". Namely, the neuron learns to be more prone to generate spikes given those combinations…
The analysis of network dynamics is oftentimes restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between behavior of systems with one-dimensional internal dynamics and with…
We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…
In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…
Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power…
Bifurcations leading to complex dynamical behaviour of non-linear systems are often encountered when the characteristics of feedback circuits in the system are varied. In systems with many unknown or varying parameters, it is an…
Information processing in the brain crucially depends on encoding properties of single neurons, with particular relevance of the spike-generation mechanism. The latter hinges upon the bifurcation type at the transition point between resting…
Phosphorylation networks, representing the mechanisms by which proteins are phosphorylated at one or multiple sites, are ubiquitous in cell signalling and display rich dynamics such as unlimited multistability. Dual-site phosphorylation…
The objective of this paper is to study the dynamical behaviour systematically of an ecological system with Beddington-DeAngelis functional response which avoids the criticism occurred in the case of ratio-dependent functional response at…