相关论文: A singular perturbation analysis for the Brusselat…
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary…
Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that…
We consider a stochastic version of the so-called Brusselator - a mathematical model for a two-dimensional chemical reaction network - in which one of its parameters is assumed to vary randomly. It has been suggested via numerical…
We prove that the famous diffusive Brusselator model can support more complicated spatial-temporal wave structure than the usual temporal-oscillation from a standard Hopf bifurcation. In our investigation, we discover that the diffusion…
In this paper we are going to make an analytical and numerical analysis for the Thomas system. Physically, this system describes a particle, driving by a system of oscillators, dissipated by a dissipation term b > 0. Mathematically, this…
The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
Researchers have developed hybrid Van der Pol Rayleigh Duffing type oscillators to model human induced forces; however, their analytical framework has largely relied on the Lindstedt Poincare perturbation method, energy balance approaches,…
A density oscillator exhibits limit-cycle oscillations driven by the density difference of the two fluids. We performed two-dimensional hydrodynamic simulations with a simple model, and reproduced the oscillatory flow observed in…
We investigate the Brusselator system with diffusion and Dirichlet boundary conditions on one dimensional space interval. Our proof demonstrates that, for certain parameter values, a periodic orbit exists. This proof is computer-assisted…
The Brusselator is a generic reaction-diffusion model for a tri-molecular chemical reaction. We consider the case when the input and output reactions are slow. In this limit, we show the existence of $K$-periodic, spatially bi-stable…
In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the blow-up method we provide a detailed description of the periodicity of the earthquake…
Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB refers to a bifurcation arising in singular perturbation…
We investigate the singular behavior of information flow near the Hopf bifurcation point by analyzing the learning rate, a key quantity in stochastic thermodynamics. As a model system exhibiting the Hopf bifurcation, we study the…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a one-dimensional unit with a bistable…
We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…
The Tantalus Oscillator is a non linear hydrodynamic oscillator with an attractive limit cycle. In this study we pursue the construction of a biparametric bifurcation diagram for the Tantalus Oscillator under biphasics perturbations. That…
The Brusselator model are used for the study of the intrinsic fluctuations of chemical reactions with different approaches. The equilibrium states of systems are assumed to be spirally stable in mean-field description, and two statistical…
Singular exponential nonlinearities of the form $e^{h(x)\epsilon^{-1}}$ with $\epsilon>0$ small occur in many different applications. These terms have essential singularities for $\epsilon=0$ leading to very different behaviour depending on…