Related papers: Hopf Bifurcation in Structural Population Models
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
A general FitzHugh-Rinzel model, able to describe several neuronal phenomena, is considered. Linear stability and Hopf bifurcations are investigated by means of the spectral equation for the ternary autonomous dynamical system and the…
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given…
In this paper, we consider the dynamics of a delayed reaction-diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary…
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…
It is well-established that shear flows are linearly unstable provided the viscosity is small enough, when the horizontal Fourier wave number lies in some interval, between the so-called lower and upper marginally stable curves. In this…
For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…
This paper presents an analysis on nonstandard generalized Hopf bifurcation in a class of switched systems where the lost of stability of linearized systems is not due to the crossing of their complex conjugate eigenvalues but relevant to…
We examine the dynamics of solutions to nonlinear Schrodinger/Gross-Pitaevskii equations that arise due to Hamiltonian Hopf (HH) bifurcations--the collision of pairs of eigenvalues on the imaginary axis. To this end, we use inverse…
We investigate the steady-state solution and its bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed…
On base of Hamiltonian formalism, we show that Hopf bifurcation arrives, in the course of the system evolution, at creation of revolving region of the phase plane being bounded by limit cycle. A revolving phase plane with a set of limit…
Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dynamical system is very sensitive to…
In this paper we analyze a generic dynamical system with $\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from…
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…
Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any…
Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay…
In this paper we study the dynamics of the monoscale Lorenz-96 model using both analytical and numerical means. The bifurcations for positive forcing parameter $F$ are investigated. The main analytical result is the existence of Hopf or…
We discuss an approach to the computer assisted proof of the existence of branches of stationary and periodic solutions for dissipative PDEs, using the Brussellator system with diffusion and Dirichlet boundary conditions as an example, We…
In this paper, we study degenerate Hopf bifurcations in a class of parametrized retarded functional differential equations. Specifically, we are interested in the case where the eigenvalue crossing condition of the classical Hopf…