Related papers: Stability enhanced by transient attractors in a me…
Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph…
In this paper, we introduce some interesting features of a memristor CNN (Cellular Neural Network). We first show that there is the similarity between the dynamics of memristors and neurons. That is, some kind of flux-controlled memristors…
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as…
Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…
A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of…
Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic…
To study a chaotic itinerant motion among varieties of ordered states, we propose a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line, and a Markov chain with a transition…
We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
The collision of a fixed point with a switching manifold (or border) in a piecewise-smooth map can create many different types of invariant sets. This paper explores two techniques that, combined, establish a chaotic attractor is created in…
For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". In high-dimensional chaotic attractors, trajectories are…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…
In this paper, we present a unified framework of multiple attractors including multistability, multiperiodicity and multichaos. Multichaos, which means that the chaotic solution of a system lies in different disjoint invariant sets with…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
Natural animal behavior displays rich lexical and temporal dynamics, even in a stable environment. This implies that behavioral variability arises from sources within the brain, but the origin and mechanics of these processes remain largely…
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…
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…
We consider transport properties of the chaotic (strange) attractor along unfolded trajectories of the dissipative standard map. It is shown that the diffusion process is normal except of the cases when a control parameter is close to some…
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control…