相关论文: A singular perturbation analysis for the Brusselat…
We use an extension of the van der Pol oscillator as an example of a system with multiple time scales to study the susceptibility of its trajectory to polynomial perturbations in the dynamics. A striking feature of many nonlinear,…
We propose general conditions for the emergence of Turing patterns in a domain that changes size through homogeneous growth/shrinkage based on the qualitative changes of a potential function. For this part of the work, we consider the most…
Typically, the period-doubling bifurcations exhibited by nonlinear dissipative systems are observed when varying systems' parameters. In contrast, the period-doubling bifurcations considered in the current research are induced by changing…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
Lienard systems of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with f(x) an even continous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak ($\epsilon\to 0$) and in the strongly…
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…
A parameter dependent perturbation of the spectrum of the scalar Laplacian is studied for a class of nonlocal and non-self-adjoint rank one perturbations. A detailed description of the perturbed spectrum is obtained both for Dirichlet…
Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the…
In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
Within the framework of the frozen temperature approximation we develop a strongly-nonlinear theory of one-dimensional pattern formation during directional solidification of binary mixture under nonequilibrium segregation. In the case of…
In this paper, we consider a coupled Brusselator model of chemical reactions, for which no symmetry for the coupling matrices is assumed. We show that the model can undergoes a Hopf bifurcation, and consequently periodic solutions can arise…
We analytically and numerically investigate the evolutions of the scalar perturbations through the cycles with nonsingular bounce. It is found that the amplitude of the curvature perturbation on large scale will be amplified cycle by cycle,…
The existence of a global attractor for the solution semiflow of the extended Brusselator system in the $L^2$ phase space is proved, which is a cubic-autocatalytic and partially reversible reaction-diffusion system with linear coupling…
We demonstrate that strongly asymmetric limit cycles can be observed in the system of three identical ring oscillators (3-gene networks known as Repressilators) globally coupled by signal molecule diffusion added to the model in a way like…
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly…
We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators $B_{1,2}$ tend to differential operators of order $l_{2,1}$, respectively, the singularity is…
We consider both the dynamics within and towards the supercycle attractors along the period-doubling route to chaos to analyze the development of a statistical-mechanical structure. In this structure the partition function consists of the…
We study the number of limit cycles and the bifurcation diagram in the Poincar\'{e} sphere of a one-parameter family of planar differential equations of degree five $\dot {\bf x}=X_b({\bf x})$ which has been already considered in previous…