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We study the structure and properties of the chimera states in the ensembles of chaotic oscillators with nonlocal coupling. It is shown that the phase and amplitude chimera states in the ensembles of chaotic oscillators with nonhyperbolic and hyperbolic attractors can be obtained using the models in the forms of two-dimensional Henon and Lozi maps. The mechanisms of birth, the structure, and the lifetime of the phase and amplitude chimeras and the regime of solitary states are studied. The chimera states in two coupled ensembles of chaotic maps are considered. The possibility of realizing a new type of the chimera structure, namely, the chimera consisting of the solitary states is demonstrated. The effects of the external and mutual synchronizations of the chimera states are described by an example of two coupled ensembles of logistic maps with nonlocal coupling. A qualitative analogy of the obtained results with the classical effect of synchronization of periodic self-sustained oscillations is discussed.

One of the important applications of chaotic oscillators is their employment as sources of entropy for True Random Bit Generators (TRBGs). In this work, we introduce high-speed TRBGs realized on a modular Field Programmable Gate Array (FPGA) hardware platform using two different switching-type chaotic oscillators. While both oscillators are autonomous, one is 3-D and the other is 4-D. This enables us to investigate and compare the advantages/disadvantages of higher dimensional chaotic oscillators on the throughput, hardware requirements and security of the generated bit-streams. For that purpose, two different implementations are described for each TRBG; a throughput-optimized architecture and a resource-optimized architecture that utilizes fewer FPGA blocks. In both cases, high speed is achieved by concatenating all state-space variables of each chaos generator into one variable. Furthermore, a new postprocessing method that enables the generated bit-streams to pass all NIST 800.22 statistical tests is introduced. Experimental results show that the throughput-optimized TRBG architecture, based on the 4-D system, can exceed 1882 Mbit/s. However, the resource-optimized TRBG architecture, based on the 3-D system, is the best in terms of FPGA resources and overall Figure of Merit.

Quick recovery of the information signals in secure communications restricts the hacking duration. The short synchronization convergence time is a crucial parameter for faster recovery. This paper develops a novel nonlinear finite-time synchronization control algorithm. This controller accomplishes the global finite-time multi-switching synchronization between two externally perturbed chaotic systems in the drive–response system synchronization scheme. The proposed controller assures the global convergence of the error dynamics in finite-time based on the Lyapunov theory. This implicitly guarantees the global stability of the closed loop. This paper considers Lp(0

We report enhancing of complete synchronization in identical chaotic oscillators when their interaction is mediated by a mismatched oscillator. The identical oscillators now interact indirectly through the intermediate relay oscillator. The induced heterogeneity in the intermediate oscillator plays a constructive role in reducing the critical coupling for a transition to complete synchronization. A common lag synchronization emerges between the mismatched relay oscillator and its neighboring identical oscillators that leads to this enhancing effect. We present examples of one-dimensional open array, a ring, a star network and a two-dimensional lattice of dynamical systems to demonstrate how this enhancing effect occurs. The paradigmatic R\"ossler oscillator is used as a dynamical unit, in our numerical experiment, for different networks to reveal the enhancing phenomenon., Comment: 10 pages, 7 figures

We investigate the transition between oscillatory and amplitude death (AD) states and the existence of death islands in intrinsic time-delayed chaotic oscillators under the simultaneous presence of diffusive (direct) and environmental (indirect) coupling. Studies in two-parameter space reveal that depending upon parameters and intrinsic time delays the coupling can bring the oscillators to the AD state and again can revive the system to oscillatory states, thus creating death islands in parameter space; this observation is in sharp contrast to the death scenario of non-delayed oscillators under the same coupling scheme where no death islands are formed. Using a linear stability analysis, we derive the explicit conditions for different transition scenarios. We use a continuation package for the time-delay systems to precisely identify the zone of AD and its islands and their origin. We also extend our study to the network of oscillators and show that the observed results are general for a large number of oscillators, too. Finally, we demonstrate our results experimentally to verify the analytical and numerical findings.

We study synchronization of two chaotic oscillators coupled with time delay in a master-slave configuration and with delayed positive feedback in the slave oscillator which acts as memory. The dynamics of the slave oscillator is analyzed with bifurcation diagrams of the peak value of the system variable with respect to the coupling and feedback strengths and two delay times. For small coupling, when the oscillators’ phases synchronize, memory can induce bistability and stabilize periodic orbits, whereas for stronger coupling it is not possible. The delayed feedback signal impairs synchronization, simultaneously enhancing coherence of the slave oscillator.

We investigate analytically and numerically coupled lattices of chaotic maps where the interaction is non-local, i.e., each site is coupled to all the other sites but the interaction strength decreases exponentially with the lattice distance. This kind of coupling models an assembly of pointlike chaotic oscillators in which the coupling is mediated by a rapidly diffusing chemical substance. We consider a case of a lattice of Bernoulli maps, for which the Lyapunov spectrum can be analytically computed and also the completely synchronized state of chaotic Ulam maps, for which we derive analytically the Lyapunov spectrum.

A class of non-diffusively coupled complex networks consisting of nodes of different dimensions is studied, in which the internal time delays are different from the coupling delays. Proper adaptive controllers are proposed for the stabilization and function matrix projective synchronization of such complex networks, respectively. The symmetric or diffusive conditions for the coupling matrices are not required. Finally, the results are applied to complex networks of chaotic oscillators showing the effectiveness of the proposed controllers.

A method for estimating the characteristics of the delayed coupling between the oscillatory systems, which is based on the empirical simulation of the phase dynamics with allowance for the phase-noise correlatedness, is proposed. The method efficiency is illustrated FOR the standard stochastic and chaotic oscillators in numerical experiments. Using this method for analyzing climatic time series, we confirm the presence of the delayed influence of the El Nino Southern oscillation on the North Atlantic Oscillation.

Akgul, Akif/0000-0001-9151-3052; istanbullu, ayhan/0000-0002-7066-4238 WOS: 000372543600003 There has recently been an increase in the number of new chaotic system designs and chaos-based engineering applications. In this study, since homoclinic and heteroclinic orbits did not exist and analyses like Shilnikov method could not be used, a 3D chaotic system without equilibrium points was included and thus different engineering applications especially for encryption studies were realized. The 3D chaotic system without equilibrium points represents a new different phenomenon and an almost unexplored field of research. First of all, chaotic system without equilibrium points was examined as the basis and electronic circuit application of the chaotic system was realized and oscilloscope outputs of phase portraits were obtained. Later, chaotic system without equilibrium points was modelled on Labview Field Programmable Gate Array (FPGA) and then FPGA chip statistics, phase portraits and oscilloscope outputs were derived. With another study, VHDL and RK-4 algorithm were used and a new FPGA-based chaotic oscillators design was achieved. Results of Labview-based design on FPGA- and VHDL-based design were compared. Results of chaotic oscillator units designed here were gained via Xilinx ISE Simulator. Finally, a new chaos-based RNG design was achieved and internationally accepted FIPS-140-1 and NIST-800-22 randomness tests were run. Furthermore, video encryption application and security analyses were carried out with the RNG designed here.

The hardware realization of a chaotic communication system from the description of continuous-time multi-scroll chaotic oscillators is introduced herein by using field-programmable gate arrays (FPGA). That way, two multi-scroll chaotic oscillators generating 2 and 6 scrolls are synchronized by applying Hamiltonian forms and observer approach. The synchronized master-slave topology is used to implement a secure communication system by adding chaos to an image at the transmission stage and by subtracting chaos at the recover stage. The FPGA realization begins by applying numerical methods to solve the system of equations describing the whole chaotic communication system. Further, the replacement of multipliers by single constant multiplication blocks reduces the use of hardware resources and accelerates the processing time as well. Using chaotic oscillators with 2 and 6 scrolls, three kinds of images are processed: one in black and white and two in gray tones. Finally, the experimental results confirm the appropriateness on realizing chaotic communication systems for image processing by using FPGAs.

The effect of parameter mismatch (diversity) taken from two-point distribution is studied numerically and theoretically in globally coupled Rossler chaotic systems. Two cases including mixed populations consisting of elements with different timescales and attractors are considered. In these two cases, the probability p of two-point distribution, which acts as an asymmetrical coupling on the system, plays a crucial role in determining the evolution of systems, and the rich dynamical phenomena are observed, especially for amplitude death (AD). The relationships between various dynamics are also discussed.

We introduce a type of cyclic coupling to investigate synchronization of chaotic oscillators. We derive analytical solutions of the critical coupling for stable synchronization under the cyclic coupling for the Rossler system and the Lorenz oscillator as paradigmatic illustration. Based on the master stability function (MSF) approach, the analytical results on critical coupling are verified numerically. An enhancing effect in terms of lowering the critical coupling or enlarging the synchronization window in a critical coupling space is noticed. The cyclic coupling is also applied in other models, Hindmarsh-Rose model, Sprott system, Chen system and forced Duffing system to confirm the enhancing effect. The cyclic coupling allows tuning of two coupling constants in reverse directions when an optimal control of synchronization is feasible.

Motivated by studies on the dynamics of heterogeneously interacting systems in neocortical neural networks, we studied heterogeneously-coupled chaotic systems. We used information-theoretic measures to investigate directions of information flow in heterogeneously coupled Rossler systems, which we selected as a typical chaotic system. In bi-directionally coupled systems, spontaneous and irregular switchings of the phase difference between two chaotic oscillators were observed. The direction of information transmission spontaneously switched in an intermittent manner, depending on the phase difference between the two systems. When two further oscillatory inputs are added to the coupled systems, this system dynamically selects one of the two inputs by synchronizing, selection depending on the internal phase differences between the two systems. These results indicate that the effective direction of information transmission dynamically changes, induced by a switching of phase differences between the two systems.

The dynamics of indirectly coupled Lorenz circuits is investigated experimentally. The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev. E 81, 046216 (2010) is verified by physical experiments with electronic circuits. Two chaotic systems coupled through a common dynamic environment shows the verity of synchronization behaviours such as anti-phase synchronization, in-phase synchronization, identical synchronization, anti-synchronization, etc.

When two different chaotic oscillators are coupled, generalized synchronization can occur. It may imply a very complicated relation between the states of drive and response systems. We propose a method that can be used to detect and characterize the generalized synchronization in modulated time-delayed systems. Using Krasovskii–Lyapunov theory, sufficient condition for generalized synchronization is derived. The proposed technique has been applied to synchronize prototype and Ikeda models by numerical simulation.

We demonstrate a neurocomputing system incorporating an amoeboid unicellular organism, the true slime mold Physarum, known to exhibit rich spatiotemporal oscillatory behavior and sophisticated computational capabilities. Introducing optical feedback applied according to a recurrent neural network model, we induce that the amoeba’s photosensitive branches grow or degenerate in a network-patterned chamber in search of an optimal solution to the traveling salesman problem (TSP), where the solution corresponds to the amoeba’s stably relaxed configuration (shape), in which its body area is maximized while the risk of being illuminated is minimized.Our system is capable of reaching the optimal solution of the four-city TSP with a high probability. Moreover, our system can find more than one solution, because the amoeba can coordinate its branches’ oscillatory movements to perform transitional behavior among multiple stable configurations by spontaneously switching between the stabilizing and destabilizing modes. We show that the optimization capability is attributable to the amoeba’s fluctuating oscillatory movements. Applying several surrogate data analyses, we present results suggesting that the amoeba can be characterized as a set of coupled chaotic oscillators.

We propose a method for determining the range of the coupling parameter for which the network of slightly nonidentical chaotic oscillators demonstrates stable synchronous behavior. As an example of using this method, we study the complete-synchronization regime of a network of nonidentical Rossler oscillators.

Chaotic oscillators with a negative-differential-resistance (NDR) subsystem having a multibranch piecewise-linear i–v characteristic (IVC) are considered. The problem of switching between chaotic oscillation regimes by changing the IVC electronically is addressed. New circuit realizations of the NDR subsystem are described in detail. It is shown that they provide highly stable IVCs.

We study how the collective dynamics of an ensemble of active coupled elements depends on the number of connections between them. We use Chua’s nonlinear oscillators as elements of this ensemble and assume nonlinear coupling. Regularization and suppression of oscillations in the transition from global to local coupling are examined.