Permutation entropy is a metric used to quantify the regularity of a time series. Here I report on its application to the problem of characterizing the behavior of a few nonlinear dynamical systems, specifically the Duffing oscillator and the Tent and Logistic maps. Numerical results indicate that the permutation entropy can in principle be used to detemine the entropy rate of a system, and thu...

A widely used approach to computability of real functions is the one in Grzegorczyk’s style originating from [1]. This approach uses computable transformations of infinitistic names of real numbers, as well as general quantifiers over these names. Other approaches allow avoiding the use of such names at least in some cases. An approach of this other kind is, for instance, the one of Tent and Zi...

Discrete time chaos based true random number generators are lightweight cryptographic primitives that offer scalable performance for the emerging low power mobile applications. In this work, a novel design method for discrete time chaos based true random number generators is developed using skew tent map as a case study. Optimum parameter values yielding maximum randomness are calculated using ...

Let T be a tent map with the slope strictly between √ 2 and 2. Suppose that the critical point of T is not recurrent. Let K denote the inverse limit space obtained by using T repeatedly as the bonding map. We prove that every homeomorphism of K to itself is isotopic to some power of the natural shift homeomorphism.

In this tutorial paper, various phenomena linked to the synchronization of chaotic systems are discussed using the simple example of two coupled skew tent maps. The phenomenon of locally riddled basins of attraction is explained using the Lyapunov exponents transversal to the synchronization manifold. The skew tent maps are coupled in two different ways, leading to quite different global dynami...

Though considerable effort has recently been devoted to hardware realization of one-dimensional chaotic systems, the influence of implementation inaccuracies is often underestimated and limited to non-idealities in the non-linear map. Here we investigate the consequences of sample-and-hold errors. Two degrees of freedom in the design space are considered: the choice of the map and the sample-an...

We investigate collective motion in high dimensional chaos, where all elements in a population behaves chaotically and incoherently in appearance. Numerical experiments for globally coupled tent maps show the existence of a quasi-periodic collective motion even under slight interaction. It is found that the amplitude of the collective motion F is scaled as, KF ∝ exp(−K−1), by the coupling stren...

As an adaptation measure to hot environments, this study proposes a cooling method that stores water inside moisture permeable waterproof designed in bag shape and promotes evaporation from its surface. In study, panel made of membrane was set under tent, experiments were conducted verify heat mitigation effects. On sunny day summer, it found the surface temperature decreased by about 7 degrees...