In the paper we describe basin of attraction p-adic dynamical system G(x) = (ax)(x+ 1). Moreover, we also describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs. Mathematics Subject Classification: 37E99, 37B25, 54H20, 12J12.

This paper presents the definition of k-error approximate entropy and proves its two basic properties, which measures the stability of chaotic pseudorandom sequences. Then the stabilities of Logistic, Hénon, Tent and Chebyshev maps are evaluated. Simulation results indicate that the approach is effective, which can distinguish the difference of stability of diverse chaotic sequences, and is an ...

Here we describe a method for separating the sum of chaotic signals into the individual components, using the inherent underlying dynamics of the chaotic sources. Capabilities of the method are demostrated on example of discrete-time systems, one-dimensional logistic maps. We demonstrate that the proposed approach based on backward iteration of the mapping equations describing the chaotic sourc...

In this work, an enhanced differential chaos shift keying (DCSK), based on a first order hybrid chaotic system, is being proposed for a high reliability underwater acoustic communication system. It can be integrated into systems that use standard existing transducers. We show that a coherent operation between the received signal and the time reversal of the basis function in a first order hybri...

Heart chaotic system and the ability of particle swarm optimization (PSO) method motivated us to benefit the method of chaotic particle swarm optimization (CPSO) to synchronize the heart three-oscillator model. It can be a suitable algorithm for strengthening the controller in presence of unknown parameters. In this paper we apply adaptive control (AC) on heart delay model, also examine the sys...

Two-dimensional cellular automata (CA) systems are widely used for modeling spatio-temporal dynamics of evolving populations. Conversely, the logistic equation is a 1-D model describing non-spatial evolution. Both clustering of individuals on CA lattice and inherent limitations of the CA model inhibit the chaotic fluctuations of average population density. We show that crude mean-field approxim...

In this paper, the D3 dihedral logistic map of fractional order is introduced. The presents a symmetry D3. It numerically shown that construction and interpretation bifurcation diagram versus requires special attention. system stability determined problem hidden attractors analyzed. Furthermore, analytical numerical results show chaotic attractor integer order, with symmetries, looses its in fr...

This paper establishes coupling between two various chaotic systems for Lorenz and Rössler circuits. The x-dynamics of circuit was coupled numerically with the x dynamics circuit. As a result optical these systems, it has been observed an exceptional variation in time series attractors, which exhibits novel behavior, leading to promises method controlling systems. However, performing fast Fouri...