Hierarchy of rational order families of chaotic maps with an invariant measure

We introduce an interesting hierarchy of rational order chaotic maps that possess an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps [1–5], with merely entropy production, the rational order chaotic maps can simultaneously produce and consume entropy. We compute the Kolmogorov-Sinai entropy of these maps analytically and also their Lyapunov exponent numerically, where the obtained numerical results support the analytical calculations.     

Generalized <Emphasis Type="Italic">N</Emphasis>-coupled maps with invariant measure in Bose-Mesner algebra perspective

By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with a given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a relation between the vertexes. Based on the E ₀ transverse projection operator, we addressed synchronization problem of an array of the linearly coupled map lattices of identical discrete time systems. The synchronization rate is determined by the second largest eigenvalue of the transition probability matrix. Algebraic properties of the Bose-Mesner algebra with an associated scheme with definite spectrum has been used in order to study the stability of the coupled map lattice. Associated schemes play a key role and may lead to analytical methods in studying the stability of the dynamical systems. The relation between the coupling parameters and the chaotic region is presented. It is shown that the feasible region is analytically determined by the number of couplings (i.e. by increasing the number of coupled maps, the feasible region is restricted). It is very easy to apply our criteria to the system being studied and they encompass a wide range of coupling schemes including most of the popularly used ones in the literature.      

Synchronization in pair-coupled maps with invariant measure

Chaos synchronization, as an important topic, has become an active research subject in non-linear science. By considering a symmetric two-dimensional map that possesses invariant measure in its diagonal and anti-diagonal invariant sub-manifolds, we have been able to introduce the most general pair-coupled map possessing invariant measure at synchronized or anti-synchronized states. Then chaotic synchronization and anti-synchronization are investigated in introduced model. We have calculated Kolmogrov–Sinai entropy and Lyapunov exponent as another tool to study the stability of pair-coupled map at synchronized and anti-synchronization states.     

Projective Synchronization of Piecewise Nonlinear Chaotic Maps

Theoretical and Mathematical Physics - With wide applications in secure data transmission and encryption, synchronization of chaotic systems is an interesting concept and has accordingly received...     

Global Synchronization & Anti-Synchronization in N-Coupled Map Lattices

By considering a symmetric N-dimensional map which possesses invariant measure in its diagonal and anti-diagonal invariant sub-manifolds, we have been able to propose an N-coupled map which possesses invariant measure in synchronized or anti-synchronized states. Then chaotic synchronization and anti-synchronization are investigated in the introduced model. We have calculated Kolmogrov–Sinai entropy and Lyapunov exponent as another tool to study the stability of N-coupled map in synchronized and anti-synchronization states.     

Thermal Quantum Discord and Super Quantum Discord Teleportation Via a Two-Qubit Spin-Squeezing Model

We study thermal quantum correlations (quantum discord and super quantum discord) in a two-spin model in an external magnetic field and obtain relations between them and entanglement. We study their dependence on the magnetic field, the strength of the spin squeezing, and the temperature in detail. One interesting result is that when the entanglement suddenly disappears, quantum correlations still survive. We study thermal quantum teleportation in the framework of this model. The main goal is investigating the possibility of increasing the thermal quantum correlations of a teleported state in the presence of a magnetic field, strength of the spin squeezing, and temperature. We note that teleportation of quantum discord and super quantum discord can be realized over a larger temperature range than teleportation of entanglement. Our results show that quantum discord and super quantum discord can be a suitable measure for controlling quantum teleportation with fidelity. Moreover, the presence of entangled states is unnecessary for the exchange of quantum information.     

A Novel Moment Approach for Calculation of the Perron–Frobenius Spectrum

The spectral properties of the Perron–Frobenius operator of the one-dimensional maps are studied by using the moment. In this paper we make an investigation into the properties of self-similar measures related to the theory of orthogonal polynomials. Numerical investigation of a particular family of maps shows that the spectrum generates the invariant measure. Analytical considerations generalize the results to a broader class of the maps. Some examples of this method are presented through out the paper.     

Type-II Intermittency from Markov Binary Block Visibility Graph Perspective

In this work, we study the type-II intermittency based on asymptotic modes and the optimized Markov binary visibility graphs perspective. In fact, we investigate the behavior of a dynamical system in the vicinity of subcritical Hopf bifurcations of pre-fixed point, fixed point, and post-fixed point using networks language. We use self maps in order to generate asymptotic modes in the type-II intermittency. We find their properties based on statistical tools such as the length between reinjection points and the mean length and also length distributions. Numerical results show that asymptotic modes affect on the trajectory and the length between reinjection points of type-II intermittency in situations of pre-fixed point, fixed point, and post-fixed point, however their mean length are approximately similar to each other. For further illustration, we compute the degree distribution of the complex network generated by type-II intermittency. Experimental results are found to agree well with the analytical results derived from the optimized Markov binary visibility graph.