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...

Fitness Dependent Optimizer (FDO) is a recent metaheuristic algorithm that mimics the reproduction behavior of bee swarm in finding better hives. This similar to Particle Swarm Optimization (PSO) but it works differently. The very powerful and has results compared other common algorithms. paper aims at improving performance FDO, thus, chaotic theory used inside FDO propose Chaotic (CFDO). Ten m...

Chaos has three important dynamic properties : the sensitive dependence on initial conditions, the intrinsic stochastic property and ergodicity. So it was applied to optimization problems. In most optimization methods such as the COA [1] and [4], variables chaos generated by different types of applications such as the Logistic, the application Tent, Lozi, Ikeda and others have shown very intere...

In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...

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...

We show that given a type α of an adding machine, for a dense set of parameters s in the interval [ √ 2, 2], if f is the tent map with slope s, then the restriction of f to the closure of the orbit of the turning point is topologically conjugate to the adding machine map of type α.

Based on the analysis of the properties of tent map, parallel chaos optimization algorithm (PCOA) using logistic map and outlook algorithm, a hybrid global optimization algorithm (PCOOA) is presented. The algorithm is structured in two stages. The first stage uses parallel chaos optimization based on tent map for global search, while outlook algorithm is employed in the second stage for local s...

The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.

In this paper, we propose a modified hybrid Salp Swarm Algorithm (SSA) and Aquila Optimizer (AO) named IHSSAO for UAV path planning in complex terrain. The primary logic of the proposed is to enhance performance AO by introducing leader mechanism SSA, tent chaotic map, pinhole imaging opposition-based learning strategy. Firstly, map utilized substitute randomly generated initial population orig...