Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability

Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled by introducing two active magnetron memristor models into the Kolmogorov-type formula.The boundness condition of the proposed hyperchaotic system is proved.Coexisting bifurcation diagram and numerical verification explain the bistability.The rich dynamics of the system are demonstrated by the dynamic evolution map and the basin.The simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented DMHS.The NIST tests show that the generated signal sequence is highly random,which is feasible for encryption purposes.Furthermore,the system is implemented based on a FPGA experimental platform,which benefits the further applications of the proposed hyperchaos.

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted （RCL-shunted） Josephson junctions （RCLSJJs） and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.

New chaotic system and its hyperchaos generation

To seek for lower-dimensional chaotic systems that have complex topological attractor structure with simple algebraic system structure, a new chaotic system of three-dimensional autonomous ordinary differential equations is presented. The new system has simple algebraic structure, and can display a 2-scroll attractor with complex topological structure, which is different from the Lorenz＇s, Chen＇s and Lu¨＇s attractors. By introducing a linear state feedback controller, the system can be controlled to generate a hyperchaotic attractor. The novel chaotic attractor, hyperchaotic attractor and dynamical behaviors of corresponding systems are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincar′e mapping and phase portrait, etc., and then verified by simulating an experimental circuit.

Hyperchaos evolved from the Liu chaotic system

This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.

A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system

This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.

ON PROPERTIES OF HYPERCHAOS: CASE STUDY

Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as the origin of complexity of dynamical systems.

Hyperchaos behaviors and chaos synchronization of two unidirectional coupled simplified Lorenz systems

To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.

A memristive map with coexisting chaos and hyperchaos

By introducing a discrete memristor and periodic sinusoidal functions,a two-dimensional map with coexisting chaos and hyperchaos is constructed.Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map,along with which other regimes of coexistence such as coexisting chaos,quasiperiodic oscillation,and discrete periodic points are also captured.The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors.Based on the nonlinear auto-regressive model with exogenous inputs(NARX)for neural network,the dynamics of the memristive map is well predicted,which provides a potential passage in artificial intelligencebased applications.

Hyperchaos of two coupled Bose-Einstein condensates with a three-body interaction

We investigate the dynamics of two tunnel-coupled Bose-Einstein condensates （BECs） in a double-well potential. The effects of the three-body recombination loss and the feeding of the condensates from the thermal cloud are studied in the case of attractive interatomic interaction. An imaginary three-body interaction term is considered and a two-mode approximation is used to derive three coupled equations which describe the total atomic numbers of the two condensates, the relative population and relative phase respectively. Theoretical analyses and numerical calculations demonstrate the existence of chaotic and hyperchaotic behaviour by using a periodically time-varying scattering length.

Synchronizing of Hyperchaos by White Noise

Chaotic synchronization can be achieved by large enough external noise strength.It is shown that a pair of generic systems in the same potential evolving to equilibrium thr-ough standard Langevin dynamics with the same noise collapse into the same orbits at longtime.We now extend the above idea to two identical hyperchaotic systems of generalizedvan der Pol oscillator.We then have Langevin equations as follows.

Synchronizing Hyperchaos by Drive-Feedback Control

Lai and Grebogi demonstrated that by combining the Pecora-Carrool(drive-response)scheme(PISS)with the variable feedback synchronization(VFS),it is possible to synchronize two nearlyidentical hyperchaotic systems.This is called the drive-feedback synchronization(DFS).In thismethod,the feedback control is directly proportional to the difference of dynamical variable fromtwo hyperchaotie systems,and is applied to one of the systems.But in Lai and Grebogi’s work

Synchronizing Hyperchaos by Variable Feedback Control

The synchronization of chaotic nonlinear systems has attracted much attention in recent years.Practical applications are being realized in the area of secure communications.However,a few syn-chronization hyperchaos have been reported.We have extended the drive-response relationship scheme(DRRS)of chaotic synchronizationproposed by Pecora and Carroll to hyperchaos in the complex Lorenz-Haken system.But some-

Synchronizing hyperchaos and controlling hyperchaos

Recently, chaos control and applications have become one of the frontier subjects innonlinear science. The synchronization (SYNC) of chaotic systems has become afascinating topic in the control of chaos since the pioneer work was done by Pecora andCarroll and was extended later. We have made a review on progress of chaos control.Pecora and Carroll specially emphasized that the SYNC of chaotic systems can be

Synchronization of Hyperchaos by Nonlinear Feedback

This paperpoints out that synchronization of hyperchaos may be achieved by a nonlinear feedback without decomposing the original system. It applies the ideas to Rossler system, and discusses several forms of nonlinear feedback by Lyapunov function and numerical calculation.

Mid-infrared hyperchaos of interband cascade lasers

Chaos in nonlinear dynamical systems is featured with irregular appearance and with high sensitivity to initial conditions.Near-infrared light chaos based on semiconductor lasers has been extensively studied and has enabled various applications.Here,we report a fully-developed hyperchaos in the mid-infrared regime,which is produced from interband cascade lasers subject to the external optical feedback.Lyapunov spectrum analysis demonstrates that the chaos exhibits three positive Lyapunov exponents.Particularly,the chaotic signal covers a broad frequency range up to the GHz level,which is two to three orders of magnitude broader than existed mid-infrared chaos solutions.The interband cascade lasers produce either periodic oscillations or low-frequency fluctuations before bifurcating to hyperchaos.This hyperchaos source is valuable for developing long-reach secure optical communication links and remote chaotic Lidar systems,taking advantage of the high-transmission windows of the atmosphere in the mid-infrared regime.

Simulation study on hyperchaos analysis of reforming system based on single-ring erbium-doped fiber laser

A reforming dynamic system based on the single-ring erbium-doped fiber laser is proposed in this paper. The reforming system has larger Lyapunov exponent and better pseudorandom characteristics according to the simulation results. It is promising in the application of the image encryption and secret communication.

CONTROLLING HYPERCHAOS IN A NEW HYPERCHAOTIC SYSTEM

In this paper,the control strategies for a new hyperchaotic system is investiga-ted. Several kinds of feedback controllers are constructed,such as the linear,speed,nonlinear doubly-periodic function feedback controllers. These controllers are used to prevent the new hyperchaos becoming an unstable equilibrium. Finally,numerical simulations are used to verify the effectiveness of the proposed controllers.

A post-processing method for true random number generators based on hyperchaos with applications in audio-based generators

True random number generators(TRNG)are important counterparts to pseudorandom number generators(PRNG).especially for high security applications such as cryptography.They produce unpredictable,non-repeatablerandom sequences.However,most TRNGs require specialized hardware to extract entropy from physical phenomena and tend to be slower than PRNGs.These generators usually require post-processing algorithms to eliminate biases but in tun.reduces performance.In this paper.a newpost-processing method based on hyperchaos is proposed forsoftware-based TRNGs which not only eliminates statisticalbiases but also provides amplification in order to improve the performance of TRNGs.The proposed method utilizes the inherent characteristics of chaos such as hypersensitivity to input shanugeri,diffusisn,and csnfusion sapabilities to ushievethese goals.Quantized bits of a physical entropy source areused to perturb the parameters of a hyperchaotic map,which is then iterated to produce a set of random output bits.To de-pict the feasibility of the proposed post-processing algorithm.it is applied in designing TRNGs based on digital audio.Thegenerators are analyzed to identify statistical defects in addition to forward and backward security.Results indicate that the proposed generators are able to produce secure true random sequences at a high throughput,which in turn reflects on the effectiveness of the proposed post-processing method.

A novel fractional-order hyperchaotic complex system and its synchronization

A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The proposed system has different numbers of equilibria for different ranges of parameters. The dynamics of the proposed system is investigated by means of phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The results show abundant dynamical characteristics. Particularly, the phenomena of extreme multistability as well as hidden attractors are discovered. In addition, the complex generalized projective synchronization is implemented between two fractional-order hyperchaotic complex systems with different fractional orders. Based on the fractional Lyapunov stability theorem, the synchronization controllers are designed, and the theoretical results are verified and demonstrated by numerical simulations. It lays the foundation for practical applications of the proposed system.

A new Rsslor hyperchaotic system and its realization with systematic circuit parameter design

Based on two modified Rosslor hyperchaotic systems, which are derived from the chaotic Rosslor system by introducing a state feedback controller, this paper proposes a new switched Rosslor hyperchaotic system. The switched system contains two different hyperchaotic systems and can change its behaviour continuously from one to another via a switching function. On the other hand, it presents a systematic method for designing the circuit of realizing the proposed hyperchaotic system. In this design, circuit state equations are written in normalized dimensionless form by rescaling the time variable. Furthermore, an analogous circuit is designed by using the proposed method and built for verifying the new hyperchaos and the design method. Experimental results show a good agreement between numerical simulations and experimental results.