Related papers: Chaotic iterations and topological chaos
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
In this paper the chaos persistence in a class of discontinuous dynamical systems of fractional-order is analyzed. To that end, the Initial Value Problem is first transformed, by using the Filippov regularization [1], into a set-valued…
We present a definition of chaotic Delone set, and establish the genericity of chaos in the space of $(\epsilon,\delta)$-Delone sets for $\epsilon\geq \delta$. We also present a hyperbolic analogue of the cut-and-project method that…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
In this paper, a new concept, i.e. ultra-chaos, is proposed for the first time. Unlike a normal-chaos, statistical properties such as the probability density functions (PDF) of an ultra-chaos are sensitive to tiny disturbances. We…
Hierarchic properties of chaotic scattering in a model of satellite encounters, studied first by Petit and Henon, are examined by decomposing the dwell time function and comparing scattering trajectories. The analysis reveals an…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to…
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
Previous research on nonlinear oscillator networks has shown that chaos synchronization is attainable for identical oscillators but deteriorates in the presence of parameter mismatches. Here, we identify regimes for which the opposite…
Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
Internet communication systems involving cryptography and data hiding often require billions of random numbers. In addition to the speed of the algorithm, the quality of the pseudo-random number generator and the ease of its implementation…
A new type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)]. It is characterized by nearly constant laminar phases, which are…
The purpose of the present paper is to introduce and establish a notion of stability for the backward propagation of chaos with respect to (initial) data sets. Consider, for example, a sequence of discrete-time martingales converging to a…