Type Of Chaos Synchronization Research Articles

Delta synchronization of Poincaré chaos in gas discharge-semiconductor systems.

We introduce a new type of chaos synchronization, specifically the delta synchronization of Poincaré chaos. The method is demonstrated for the irregular dynamics in coupled gas discharge-semiconductor systems (GDSSs). It is remarkable that the processes are not generally synchronized. Our approach entirely relies on ingredients of the Poincaré chaos, which in its own turn is a consequence of the unpredictability in Poisson stable motions. The drive and response systems are in the connection, such that the latter is processed through the electric potential of the former. The absence of generalized synchronization between these systems is indicated by utilizing the conservative auxiliary system. However, the existence of common sequences of moments for finite convergence and separation confirms the delta synchronization. This can be useful for complex dynamics generation and control in electromagnetic devices. A bifurcation diagram is constructed to separate stable stationary solutions from non-trivial oscillatory ones. Phase portraits of the drive and response systems for a specific regime are provided. The results of the sequential test application to indicate the unpredictability and the delta synchronization of chaos are demonstrated in tables. The computations of the dynamical characteristics for GDSSs are carried out by using COMSOL Multiphysics version 5.6 and MATLAB version R2021b.

Improved Control Schemes for Projective Synchronization of Delayed Neural Networks with Unmatched Coefficients

Projective synchronization (PS) is a type of chaos synchronization where the states of slave system are scaled replicas of the states of master system. This paper studies the asymptotic projective synchronization (APS) between master–slave chaotic neural networks (NNs) with mixed time-delays and unmatched coefficients. Based on useful inequality techniques and constructing a suitable Lyapunov functional, some simple criteria are derived to ensure the APS of considered networks via designing a novel adaptive feedback controller. In addition, a numerical example and its MATLAB simulations are provided to check the feasibility of the obtained results. The main innovation of our work is that we dealt with the APS problem between two different chaotic NNs, while most of the existing works only concerned with the PS of chaotic systems with the same topologies. In addition, compared with the controllers introduced in the existing papers, the designed controller in this paper does not require any knowledge about the activation functions, which can be seen as another novelty of the paper.

A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems

Abstract Referring to incommensurate fractional-order systems, this paper proposes a new type of chaos synchronization by combining full state hybrid function projective synchronization (FSHFPS) and inverse full state hybrid function projective synchronization (IFSHFPS). In particular, based on stability theory of linear integer-order systems and stability theory of linear fractional-order systems, the co-existence of FSHFPS and IFSHFPS between incommensurate fractional chaotic (hyperchaotic) systems is proved. To illustrate the capabilities of the novel approach proposed herein, numerical and simulation results are given.

N-Systems Function Projective Combination Synchronization—A Review of Real and Complex Continuous Time Chaos Synchronization

As an important branch in the field of chaos, chaos synchronization (CHS) has attracted great attentions since it was firstly proposed. In this review article, numerous types of continuous time CHS are presented for the past 29 years. Previous CHS are divided into two major parts: one is CHS in real number field, and the other is CHS in complex number field. Some classic types of CHS, controllers and corresponding stability theories are preliminarily reviewed. Besides, a new type of chaos synchronization is proposed, which is called N-systems combination function projective synchronization (NCOFPS). Interestingly and importantly, most of these proposed types of CHS belong to NCOFPS. Then, time delay function projective synchronization (TDFPS) is also proposed, which is one of the types of NCOFPS and never studied in existed papers. And TDFPS controller, corresponding mathematical proof are obtained and simulation experiments illustrate the effectiveness of investigated controller. This paper provides a generalized view to catch the development of CHS in different fields. Finally, we give the conclusions and prospects of CHS.

New type of chaos synchronization in discrete-time systems: the F-M synchronization

AbstractIn this paper, a new type of synchronization for chaotic (hyperchaotic) maps with different dimensions is proposed. The novel scheme is called F – M synchronization, since it combines the inverse generalized synchronization (based on a functional relationship F) with the matrix projective synchronization (based on a matrix M). In particular, the proposed approach enables F – M synchronization with index d to be achieved between n-dimensional drive system map and m-dimensional response system map, where the synchronization index d corresponds to the dimension of the synchronization error. The technique, which exploits nonlinear controllers and Lyapunov stability theory, proves to be effective in achieving the F – M synchronization not only when the synchronization index d equals n or m, but even if the synchronization index d is larger than the map dimensions n and m. Finally, simulation results are reported, with the aim to illustrate the capabilities of the novel scheme proposed herein.

Different types of synchronization in coupled network based chaotic circuits

We propose a simple and new unified method to achieve lag, complete and anticipatory synchronizations in coupled nonlinear systems. It can be considered as an alternative to the subsystem and intentional parameter mismatch methods. This novel method is illustrated in a unidirectionally coupled RC phase shift network based Chua’s circuit. Employing feedback coupling, different types of chaos synchronization are observed experimentally and numerically in coupled identical chaotic oscillators without using time delay. With a simple switch in the experimental set up we observe different kinds of synchronization. We also analyze the coupled system with numerical simulations.

On Λ −ϕ generalized synchronization of chaotic dynamical systems in continuous–time

In this paper, a new type of chaos synchronization in continuous-time is proposed by combining inverse matrix projective synchronization (IMPS) and generalized synchronization (GS). This new chaos synchronization type allows us to study synchronization between different dimensional continuous-time chaotic systems in different dimensions. Based on stability property of integer-order linear continuous-time dynamical systems and Lyapunov stability theory, effective control schemes are introduced and new synchronization criterions are derived. Numerical simulations are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.

Chaos synchronization in networks of semiconductor superlattices

Chaos synchronization has been demonstrated as a useful building block for various tasks in secure communications, including a source of all-electronic ultrafast physical random number generators based on room temperature spontaneous chaotic oscillations in a DC-biased weakly coupled GaAs/Al0.45Ga0.55As semiconductor superlattice (SSL). Here, we experimentally demonstrate the emergence of several types of chaos synchronization, e.g. leader-laggard, face-to-face and zero-lag synchronization in network motifs of coupled SSLs consisting of unidirectional and mutual coupling as well as self-feedback coupling. Each type of synchronization clearly reflects the symmetry of the topology of its network motif. The emergence of a chaotic SSL without external feedback and synchronization among different structured SSLs open up the possibility for advanced secure multi-user communication methods based on large networks of coupled SSLs.

A New Generalized-Type of Synchronization for Discrete-Time Chaotic Dynamical Systems

In this paper, a new type of chaos synchronization in discrete-time is proposed by combining matrix projective synchronization (MPS) and generalized synchronization (GS). This new chaos synchronization type allows us to study synchronization between different dimensional discrete-time chaotic systems in different dimensions. Based on nonlinear controllers and Lyapunov stability theory, effective control schemes are introduced and new synchronization criterions are derived. Numerical simulations are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.

Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters

This paper focuses on the adaptive modified hybrid function projective synchronization with complex function transformation matrix (CMHFPS) for different dimensional chaotic (hyperchaotic) systems with complex variables and unknown complex parameters. The chaotic systems are considerably different from those in the existing closely related literature. Moreover, the transformation matrix in this type of chaos synchronization is not a square matrix, and its elements are complex functions. In particular, by constructing appropriate Lyapunov functions dependent on complex variables, the adaptive controllers are designed to synchronize different dimensional complex chaos (hyperchaos) with complex parameters in the sense of CMHFPS, and the complex update laws for estimating unknown complex parameters of complex chaotic systems are also given. Finally, two examples are presented to illustrate the effectiveness and feasibility of the theoretical results.

Complex modified generalized projective synchronization of fractional-order complex chaos and real chaos

This paper introduces a type of modified generalized projective synchronization with complex transformation matrix (CMGPS) for fractional-order complex chaos and real chaos with the same dimension and different structures. The transformation matrix in this type of chaos synchronization is a non-diagonal square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, necessary and sufficient criteria are established to guarantee CMGPS for the fractional-order complex chaos and fractional-order real chaos, and for two fractional-order complex chaotic systems, respectively. Numerical examples are provided to illustrate the feasibility and effectiveness of our theoretical results.

Synchronization of Discrete Chaotic Systems via Double Scaling Matrix in Different Dimensions

In this paper, a new type of chaos synchronization in discrete-time is proposed when the scaling functions in Q-S synchronization are replaced by two suitable matrices. This new synchronization type allows us to study synchronization between different dimensional discrete chaotic systems in different dimensions. By using Lyapunov stability theory and nonlinear controllers, new results are derived. Numerical simulations are used to verify the effectiveness of the theoritical results and the proposed schemes derived in this paper.

Chaos Based Optical Communication

 Abstract—Chaos based communication has been a very attractive research field from last couple of decades due to its potential of providing secure communication. In this paper, we reviewed principles and theory governing the field of chaos. We studied governing principles and different methods for chaotic signal generation and schemes used to modulate message signal with chaotic signal in optical fiber communication systems. We also reviewed the principal concepts governing chaos synchronization, types of chaos synchronization and some proposed techniques used for the synchronization of transmitter and receiver in optical fiber communication systems.

Function Synchronization of the Fractional-Order Chaotic System

Function synchronization is an important type of chaos synchronization because of enhancing the security of communication. In order to obtain the better conformances of function synchronization, a method of the fractional-order chaotic system is presented, which based on the stability theory of the fractional order system. This method need construct a parameter matrix and a coupled matrix using fractional-order chaotic drive system at first, and then the chaotic response system is set up with these matrixes. The synchronization error function between drive system and response system is satisfied with the asymptotic stability. Function synchronization of the fractional-order Rikitake chaotic system is selected as a typical example. Numerical simulation results demonstrate the validity of the presented method. This method not only has better synchronization conformances, but also can be applied in the chaotic secure communications.

Hybrid Projective Synchronization of a New Hyperchaotic System

The full state hybrid projective synchronization, which includes complete synchronization, anti-synchronization and projective synchronization as its special item, is a novel type of chaos synchronization, so the research in this area has high practical significance. This paper is involved with full state hybrid projective synchronization of a new hyperchaotic system. Based on the stability criterion of linear system, full state hybrid projective synchronization is achieved by appropriate linear separation. Numerical simulation is presented to demonstrate the effectiveness of the proposed method.

A new scheme of general hybrid projective complete dislocated synchronization

Based on the Lyapunov stability theorem, a new type of chaos synchronization, general hybrid projective complete dislocated synchronization (GHPCDS), is proposed under the framework of drive-response systems. The difference between the GHPCDS and complete synchronization is that every state variable of drive system does not equal the corresponding state variable, but equal other ones of response system while evolving in time. The GHPCDS includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. As examples, the Lorenz chaotic system, Rössler chaotic system, hyperchaotic Chen system and hyperchaotic Lü system are discussed. Numerical simulations are given to show the effectiveness of these methods.

Propagation of projective synchronization in a series connection of chaotic systems

Projective synchronization is a type of chaos synchronization where the response system states are scaled replicas of the drive system states. This paper deals with the propagation of projective synchronization in a series connection of N chaotic discrete-time drive systems and N response systems. By exploiting an observer-based approach, the paper demonstrates that dead-beat projective synchronization (i.e., exact synchronization in finite time for any scaling factor) is achieved between the n th drive and n th response systems. In particular, it is shown that projective synchronization starts from the innermost ( N th) drive–response system pair and propagates toward the outermost (first) drive–response system pair. Only a single scalar synchronizing signal connects the cascaded drive and response systems. Finally, an example illustrates the propagation of different types of chaos synchronization in a series connection consisting of a Gingerbreadman map, a third order hyperchaotic Henon map and a Lozi map.

Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems

Chaos synchronization, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, chaos synchronization between nonlinear systems has been extensively studied, and many types of synchronization have been announced. This paper introduces another novel type of chaos synchronization – full state hybrid projective synchronization (FSHPS), which includes complete synchronization, anti-synchronization and projective synchronization as its special item. Based on the Lyapunov’s direct method, the general FSHPS scheme is given and illustrated with Lorenz chaotic system and hyperchaotic Chen system as examples. Numerical simulations are used to verify the effectiveness of the proposed scheme.

Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback.

We have investigated the transient characteristics of two types of chaos synchronization in a semiconductor laser subject to optical feedback: complete synchronization and strong injection locking-type synchronization. We have calculated the statistical distribution of the transient response time of synchronization when the initial position in the starting attractor is varied. For complete synchronization, the distribution of the transient response time has much larger average and variance than the average period of the chaotic oscillations. Conversely, a short transient response time is obtained for strong injection locking-type synchronization. We found that the transient response time is dependent upon the maximum Lyapunov exponent of the chaotic temporal waveform for complete synchronization, whereas it is almost constant for strong injection locking-type synchronization.

Inverse anticipating chaos synchronization.

We derive conditions for achieving inverse anticipating synchronization where a driven time-delay chaotic system synchronizes to the inverse future state of the driver. The significance of inverse anticipating chaos in delineating synchronization regimes in time-delay systems is elucidated. The concept is extended to cascaded time-delay systems.