相关论文: A singular perturbation analysis for the Brusselat…

Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell…

Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these…

Experimental evidence of an absorbing phase transition, so far associated with spatio-temporal dynamics is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed opto-electronic feedback and…

Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is $\sim $40 kyr before the so-called middle…

We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…

We study the bifurcation diagram of the Onsager free-energy func- tional for liquid crystals with orientation parameter on the sphere in three dimensions. In particular, we concentrate on a very general class of two- body interaction…

We study the Rolie-Poly model for entangled polymers, using a singular perturbation analysis for the limit of large relaxation time. In this limit, it is shown that the model displays the characteristic features of thixotropic yield stress…

This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider auto-oscillations arising on the level of enzyme-substrate interactions in the nutrient and respiratory…

The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical…

We study a class of multi-parameter three-dimensional systems of ordinary differential equations that exhibit dynamics on three distinct timescales. We apply geometric singular perturbation theory to explore the dependence of the geometry…

We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this…

For a class of $(N+1)$-dimensional systems of differential delay equations with a cyclic and monotone negative feedback structure, we construct a two-dimensional invariant manifold, on which phase curves spiral outward towards a bounding…

We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expansion around the fixed point and the bifurcation parameter,…

We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…

In this paper, we studied Rayleigh autonomous oscillator by searching its limit cycle and by studying the stability of the cycle. Through this study, we studied the fixed points of the equation of Rayleigh oscillator and we realized that in…

We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and…

We study the simplest mode-coupling equation which describes the time correlation function of the spherical p-spin glass model. We formulate a systematic perturbation theory near the mode-coupling transition point by introducing multiple…

A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…

We study the radial relaxation dynamics toward equilibrium and time-periodic pulsating spherically symmetric gas bubbles in an incompressible liquid due to thermal effects. The asymptotic model ([A. Prosperetti, J. Fluid Mech., 1991] and…

We find an upper bound for the number of limit cycles, bifurcating from the 8-loop of the Duffing oscillator $x"= x-x^{3}$ under the special cubic perturbation $$ x"= x-x^{3}+\lambda_{1}y+\lambda_{2}x^{2}+\lambda_{3}xy+\lambda_{4}x^{2}y .…