Related papers: Bifurcation Analysis in a Continuous-Time Informat…
Information spread on networks can be efficiently modeled by considering three features: documents' content, time of publication relative to other publications, and position of the spreader in the network. Most previous works model up to…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…
We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based…
Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…
We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of…
This paper investigates the dynamic behavior of a simplified single reed instrument model subject to a stochastic forcing of white noise type when one of its bifurcation parameters (the dimensionless blowing pressure) increases linearly…
The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence…
An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by…
Time lags are ubiquitous in biophysiological processes and more generally in real-world complex networks. It has been recently proposed to use information-theoretic tools such as transfer entropy to detect and estimate a possible delay in…
In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the…
In the context of a spatially extended model for the electrical activity in a pituitary lactotroph cell line, we establish that two delayed bifurcation phenomena from ODEs ---folded node canards and slow passage through Hopf bifurcations---…
Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
For systems of delay differential equations the Hopf bifurcation was investigated by several authors. The problem we consider here is that of the possibility of emergence of a codimension two bifurcation, namely the Bautin bifurcation, for…
We study a reaction-advection-diffusion model of a target-offender-guardian system designed to capture interactions between urban crime and policing. Using Crandall-Rabinowitz bifurcation theory and spectral analysis, we establish rigorous…
We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear…
Bursting is a periodic transition between a quiescent state and a state of repetitive spiking. The phenomenon is ubiquitous in a variety of neurophysical systems. We numerically study the dynamical properties of a normal form of subcritical…
Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or…
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of…