相关论文: Magic Number 7 +- 2 in Globally Coupled Dynamical …
Dominance of Milnor attractors in high-dimensional dynamical systems is reviewed, with the use of globally coupled maps. From numerical simulations, the threshold number of degrees of freedom for such prevalence of Milnor attractors is…
Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase.…
Information processing by random feed-forward networks consisting of units with sigmoidal input-output response is studied by focusing on the dependence of its outputs on the number of parallel paths M. It is found that the system leads to…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
Cells possess non-membrane-bound bodies, many of which are now understood as phase-separated condensates. One class of such condensates is composed of two polymer species, where each consists of repeated binding sites that interact in a…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e.…
We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven…
Due to errors of numerical methods, qualitative behavior of the numerically simulated solution may be completely different from qualitative behavior of the real trajectory. Therefor in study of attractors the more useful idea is to simulate…
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…
The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. We…
Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize the riddled basin using the uncertainty…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
A system of N unidimensional global coupled maps (GCM), which support multiattractors is studied. We analize the phase diagram and some special features of the transitions (volume ratios and characteristic exponents), by controlling the…
We study chaotic dynamics in a system of four differential equations describing the dynamics of five identical globally coupled phase oscillators with biharmonic coupling. We show that this system exhibits strange spiral attractors…
Modular organization characterizes many complex networks occurring in nature, including the brain. In this paper we show that modular structure may be responsible for increasing the robustness of certain dynamical states of such systems. In…
Ground-state and excited-state properties of vertically coupled double quantum dots are studied by exact diagonalization. Magic-number total angular momenta that minimize the total energy are found to reflect a crossover between electron…