Related papers: Ultradiscrete Bifurcations for One Dimensional Dyn…
We examine the interaction of transcritical and saddle-node bifurcations in a predator-prey-nutrient system that is stressed by the presence of a toxicant affecting the prey. This model, formulated by Kooi et al. ({\sl Ecol. Model.} {\bf…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
Non-minimally coupled scalar field models are well-known for providing interesting cosmological features. These include a late time dark energy behavior, a phantom dark energy evolution without singularity, an early time inflationary…
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. The potential energy surface of the system that we consider…
A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Max-plus equations are derived from tropically discretized Sel'kov model via ultradiscretization. These max-plus equations possess common dynamical structures with the discretized model: Neimark-Sacker bifurcation and limit cycles. The…
Dynamical processes induced by the external time-dependent fields can provide valuable insight into the characteristic energy scales of a given physical system. We investigate them here in a nanoscopic heterostructure, consisting of the…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i.…
Moment systems arise in a wide range of contexts and applications, e.g. in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a…
We investigate the universality in collisionless nonlinear dynamics of a codimension-two bifurcation where two eigenvalues collide at the origin, and two lines of continuous bifurcation and discontinuous jump meet. Through linear analysis…
Motivated by recent experimental progress to read out quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven anharmonic oscillator, the Duffing…
This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…
We present a black-box method to numerically investigate the linear stability of arbitrary multi-physics problems. While the user just has to enter the system's residual in weak formulation, i.e. by a finite element method, all required…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
We study the dynamics of a system defined by the Navier-Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two dimensional case. We show that more complicated bifurcations can appear in this system for a…
In this work, we focus on an autocatalytic reaction-diffusion model and carry out multiple scale weakly nonlinear analysis. A cubic and a quadratic autocatalytic reaction system is analysed. We develop a framework to identify the critical…
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems…