Related papers: Numerical Chaos in a Fractional Order Logistic Map
Many open problems in biology, as in the physical sciences, display nonlinear and 'chaotic' dynamics, which, to the extent possible, cannot be reasonably understood. Moreover, mathematical models which aim to predict/estimate unknown…
The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here we present a variety of invariant measures for quantifying chaotic dynamics in relativity by exploiting the coordinate…
By a classical result of Kathleen Alligood and James Yorke we know that as we isotopically deform a map $f:ABCD\to\mathbb{R}^2$ to a Smale horseshoe map we should often expect the dynamical complexity to increase via a period--doubling…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and…
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.
This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…
After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian…
A map to the quark-gluon cascade on the basis of nonlinearity in the quark and gluon distributions in hadrons is proposed. Calculations of the quarks trajectories have shown the presence of the chaotic dynamics as a consequence of…
A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…
In this paper, we introduce several new types and generalizations of the concepts distributional chaos and Li-Yorke chaos. We consider the general sequences of binary relations acting between metric spaces, while in a separate section we…
We study a network of logistic maps with two types of global coupling, inertial and dissipative. Features of the clusterization process are revealed and compared, which are associated with presence of each type of couplings. For the…
Chaos degree defined through two complexities in information dynamics is applied to some deterministic dynamical models. It is shown that this degree well describes the chaostic feature of the models.
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to discrete Lorenz-like and figure-eight strange attractors.…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The order of fractional derivative has been proved to be of great…
We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We provide the probabilistic representation for the non-linear…
In mesoscopic systems conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system with either fully chaotic or mixed phase space generically…