相关论文: Fractal analysis of Neimark-Sacker bifurcation

Decision making is a fundamental capability of autonomous systems. As decision making is a process which happens over time, it can be well modeled by dynamical systems. Often, decisions are made on the basis of perceived values of the…

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a…

We simulate binary soft disk systems in two dimensions, and investigate how the dynamics slow as the area fraction is increased toward the glass transition. The "fragility" quantifies how sensitively the relaxation time scale depends on the…

We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…

In this paper, we take advantage of the averaging theory to investigate a torus bifurcation in two-parameter families of 2D nonautonomous differential equations. Our strategy consists in looking for generic conditions on the averaged…

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…

We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…

We investigate a decomposition of a unital Lindblad dynamical map of an open quantum system into two distinct types of mapping on the Hilbert-Schmidt space of quantum states. One component of the decomposed map corresponds to reversible…

We study dynamical systems that switch between two different vector fields depending on a discrete variable and with a delay. When the delay reaches a problem-dependent critical value so-called event collisions occur. This paper classifies…

Dynamical properties of tropically discretized and max-plus negative feedback models are investigated. Reviewing the previous study [S. Gibo and H. Ito, J. Theor. Biol. 378, 89 (2015)], the conditions under which the Neimark-Sacker…

We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…

For any adic transformation $T$ defined on the path space $X$ of an ordered Bratteli diagram, endowed with a Markov measure $\mu$, we construct an explicit dimension space (which corresponds to a matrix values random walk on $\mathbb{Z}$)…

In this paper we study the geometry of the attractors of holomorphic maps with an irrationally indifferent fixed point. We prove that for an open set of such holomorphic systems, the local attractor at the fixed point has Hausdorff…

We consider the system -\Delta u_j + a(x)u_j = \mu_j u_j^3 + \be\sum_{k\ne j}u_k^2u_j, u_j>0, \qquad j=1,...,n, on a possibly unbounded domain $\Om\subset\R^N$, $N\le3$, with Dirichlet boundary conditions. The system appears in nonlinear…

We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…

In chemical reactions, trajectories typically turn from reactants to products when crossing a dividing surface close to the normally hyperbolic invariant manifold (NHIM) given by the intersection of the stable and unstable manifolds of a…

Dynamical systems whose symplectic structure degenerates, becoming noninvertible at some points along the orbits are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the…

We study the orientational dynamics of superparamagnetic colloidal dimers that carry both an induced magnetic moment, proportional to the applied field, and an effective permanent moment. In a static, uniform magnetic field, dimers that are…

We study a dynamical counterpart of bifurcation to invariant torus for a system of interconnected fast phase variables and slowly varying parameters. We show that in such a system, due to the slow evolution of parameters, there arise…

Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady…