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This work presents a numerical method to color the bifurcation diagram of any discrete map, based on the distribution of the map's values in its domain. This density-colored diagram reveals information on the uniformity of the map's value distribution across its domain set, as a bifurcation parameter is increased. This diagram can serve as a complementary visual tool for the analysis of chaotic maps, and can be vital for the application of chaotic dynamics. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic communication system based on the combination of Improved–Differential chaos-shift keying (IDCSK) scheme and 2 × 2 MIMO technique (2T2R), namely 2T2R-IDCSK, is investigated. We point out that there are differences in correlation characteristics between the conventional and time-reversed chaotic sequences. From this aspect, bit-error-rate (BER) performance of the system over an additive white Gaussian noise (AWGN) channel is analyzed taking into account the correlation effect of time-reversed chaotic sequences. BER expressions are verified by Monte-Carlo simulation. The obtained results prove that the 2T2R-IDCSK system performs worse under the correlation effect, however still dramatically outperforms the conventional 2 × 2 MIMO-DCSK system. [ABSTRACT FROM AUTHOR]

In the last decade, researchers, who work in the field of nonlinear circuits, have the "dream" to use a real memristor, which is the only nonlinear fundamental circuit element, in a new or other reported nonlinear circuit in literature, in order to experimentally investigate chaos. With this intention, for the first time, a well-known nonlinear circuit, in which its nonlinear element has been replaced with a commercially available memristor (KNOWM memristor), is presented in this work. Interesting phenomena concerning chaos theory, such as period-doubling route to chaos, coexisting attractors, one-scroll and double-scroll chaotic attractors are experimentally observed. [ABSTRACT FROM AUTHOR]

This paper proposes a novel chaotic system with infinite number of equilibria located on an exponential curve. It signifies an exciting category of dynamical systems which display many features of regular and chaotic motions. The proposed chaotic system belongs to the general category of chaotic systems with hidden attractors. Moreover, some theoretical analyses of the chaotic system’s dynamical characteristics are presented. Using the developed chaotic system, the new random number generator and encryption algorithm have been designed. Encryption application and security analysis are presented verifying its feasibility. [ABSTRACT FROM AUTHOR]

A new chaotic system having variable equilibrium is introduced in this paper. The presence of an infinite number of equilibrium points, a stable equilibrium, and no-equilibrium is observed in the system. Interestingly, this system is classified as a rare system with hidden attractors from the view point of computation. Complex dynamical behavior and a circuital implementation of the new system have been investigated in our work. [ABSTRACT FROM AUTHOR]

Wang-Chen system with only one stable equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang-Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one stable equilibrium to hidden attractors without equilibrium. [ABSTRACT FROM AUTHOR]

Although chaotic systems with hidden attractors have been discovered recently, there are few investigations about relationships among them. This brief work introduces a novel chaotic system with only one stable equilibrium that is constructed by adding a tiny perturbation into a known chaotic flow having hidden attractors with a line equilibrium. [ABSTRACT FROM AUTHOR]

The presence of hidden attractors in dynamical systems has received considerable attention recently both in theory and applications. A novel three-dimensional autonomous chaotic system with hidden attractors is introduced in this paper. It is exciting that this chaotic system can exhibit two different families of hidden attractors: hidden attractors with an infinite number of equilibrium points and hidden attractors without equilibrium. Dynamical behaviors of such system are discovered through mathematical analysis, numerical simulations and circuit implementation. [ABSTRACT FROM AUTHOR]

Discovering unknown features of no-equilibrium systems with hidden strange attractors is an attractive research topic. This paper presents a novel no-equilibrium chaotic system that is constructed by using a state feedback controller. Interestingly, the new system can exhibit multiwing butterfly attractors. Moreover, a new chaotic system with an infinite number of equilibrium points, which can generate multiscroll attractors, is also proposed by applying the introduced methodology. [ABSTRACT FROM AUTHOR]

In this letter we investigate the role of complex fixed-points in finding hidden attractors in chaotic flows with no equilibria. If these attractors could be found by starting the trajectory in the neighborhood of complex fixed-points, maybe it would be better not to call them hidden. [ABSTRACT FROM AUTHOR]

This paper introduces a new no-equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. The dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincaré map and period-doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without equilibria are also proposed by applying the presented methodology. [ABSTRACT FROM AUTHOR]

The dynamic behavior of bidirectionally coupled Duffing-type circuits is numerically and experimentally investigated. Two related phenomena are explored such as anti-phase synchronization and inverse π-lag synchronization. Anti-phase synchronization is observed for the first time in coupled Duffing-type systems, while the inverse π-lag synchronization phenomenon in mutually coupled identical oscillators is a new type of synchronization. Inverse π-lag synchronization can be characterized by the vanishing of the sum of two relevant periodic signals. The first one is the signal of the first circuit x1 and the second is the signal of the second circuit x2 with a time lag τmin. This time lag is equal to T/2, where T is the period of x1 and x2. The measurements and numerical computations suggest that these two synchronization phenomena are correlated with the symmetry under the transformation, x → -x, y → -y and t → t + T/2, which the Duffing equation exhibits. [ABSTRACT FROM AUTHOR]