Related papers: Numerical Chaos in a Fractional Order Logistic Map
We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on…
Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing one-step Poincar\'e map, we demonstrate that classical phase space corresponding to a single realization of the random perturbation involves domains of…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Nonlinear fractional dynamics with scale invariance in continuous and discrete time approaches are described. We use non-integer-order integro-differential operators that can be interpreted as generalizations of scaling (dilation)…
We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to…
In this paper, we investigate the dynamic emergence of traffic order in a distributed multi-agent system, aiming to minimize inefficiencies that stem from unnecessary structural impositions. We introduce a methodology for developing a…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
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…
This paper is devoted to the problem of synchronization between fractional-order chaotic systems with Gaussian fluctuation by the method of fractional-order sliding mode control. A fractional integral (FI) sliding surface is proposed for…
We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from chaotic motion on the whole measure to chaos…
Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were inspired by the behaviour of interval maps. However these…
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…
A proper discretization of the logistic differential equation, which is preserving these two distinct equilibrium solutions and their unstability and stability, suggest that we need to examine the time delay of the logistic map. According…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of…