Related papers: Hopf bifurcation from fronts in the Cahn-Hilliard …
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
We study homoclinic orbits of the Swift-Hohenberg equation near a Hamiltonian-Hopf bifurcation. It is well known that in this case the normal form of the equation is integrable at all orders. Therefore the difference between the stable and…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
In this paper, we show the existence of Hopf bifurcation of a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the…
The motion of a self-propelled particle is affected by its surroundings, such as boundaries or external fields. In this paper, we investigated the bifurcation of the motion of a camphor grain, as a simple actual self-propelled system,…
The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and…
The cyclicity problem, crucial in analyzing planar vector fields, consists in estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in…
This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try…
A reaction-diffusion-advection predator-prey model with Holling type-II predator functional response is considered. We show the stability/instability of the positive steady state and the existence of a Hopf bifurcation when the diffusion…
Hopf bifurcations in fast-slow systems of ordinary differential equations can be associated with surprising rapid growth of periodic orbits. This process is referred to as canard explosion. The key step in locating a canard explosion is to…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
A Hamilton-Jacobi equation with Caputo's time-fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic…
Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…
Using the charmonium light-front wavefunctions obtained by diagonalizing an effective Hamiltonian with the one-gluon exchange interaction and a confining potential inspired by light-front holography in the basis light-front quantization…
We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical supercritical complex Ginzburg-Landau equation, we show that…
Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…
In this paper we introduce universal asymptotic unfolding normal forms for nonlinear singular systems. Next, we propose an approach to find the parameters of a parametric singular system that they play the role of universal unfolding…
Motivated by physical and numerical observations of time oscillatory ``galloping'', ``spinning'', and ``cellular'' instabilities of detonation waves, we study Poincar\'e--Hopf bifurcation of traveling-wave solutions of viscous conservation…
We consider the free boundary problem for a liquid drop of nearly spherical shape with capillarity, and we study the existence of nontrivial (i.e., non spherical) rotating traveling profiles bifurcating from the spherical shape, where the…
Hopf bifurcations have been studied perturbatively under two broad headings, viz., super-critical and sub-critical. The criteria for occurrences of such bifurcations have been investigated using the renormalization group. The procedure has…