Hybrid Projective Synchronization Research Articles

Hybrid Projective Synchronization via PI Controller Based on DNA Strand Displacement.

Classical three-variable chaotic system coupling synchronization has been implemented in previous work based on DNA strand displacement (DSD). Herein, by using DSD reactions as the foundation, a proportional integral (PI) controller for chaotic system is introduced to realize the hybrid projective synchronization for different four-variable chaotic systems. DSD-based chaotic systems are composed of catalysis modules, annihilation modules and degradation modules for realizing the construction of chaotic attractors. PI controllers are consist of catalysis, annihilation and adjust DSD modules that are easy to modify and can be added to chaotic system for achieving hybrid projective synchronization. Our work can be acted as the reference for the investigation of chaos synchronization.

Hybrid Projective Synchronization of Fractional-Order Extended Hindmarsh–Rose Neurons with Hidden Attractors

In view of the diversity of stimulated current that neurons may experience, an extended Hindmarsh–Rose neuron model is proposed and the corresponding fractional-order neuron model, with no equilibrium point, is depicted. Additionally, various hidden attractors of the addressed neuron model are analyzed by changing system parameters and the order of fractional-order neuron system. Furthermore, hybrid projective synchronizations of the proposed neurons are investigated and schemes are obtained by designing suitable controllers according to fractional stability theory. Besides, the validity of the theoretical results is verified through numerical simulations. In short, the research results have potential application in revealing the dynamical behaviors of neuron system and controlling the behaviors of neuron into certain status.

Multistability and hidden attractors in a novel simple 5D chaotic Sprott E system without equilibrium points

This paper presents a novel simple 5D chaotic system with no critical point having hidden attractors which are derived via state feedback control strategy from the known 3D Sprott-E system. The proposed system is different from some well-known hidden chaotic systems, it exhibits chaotic 2-torus and consists of nine terms including only one control parameter, two nonlinear terms. Some dynamical behaviors of this system were analyzed theoretically and numerical simulations such as equilibrium points, Lyapunov exponents, Lyapunov dimension, phase portraits, multistability, and hybrid projective synchronization.

Controlling hyperchaos in non-identical systems using active controlled hybrid projective combination-combination synchronization technique

The current manuscript investigates a hybrid projective combination-combination synchronization scheme (HPCCSS) in four different hyperchaotic (HC) systems via active control technique (ACT). In view of Lyapunov stability theory (LST), the discussed strategy determines asymptotic stability globally. Also, numerous synchronization schemes, namely, projective synchronization, chaos control issue, combined synchronization, and many more turn into specific kinds for combination-combination (C-C) synchronization. Also, a comparison analysis within the given HPCCSS and prior published literature has been done. The proposed scheme has applications in secure communication as well as encryption. Additionally, numerical simulation is executed to check the efficiency of considered scheme using MATLAB software.

An investigation on microscopic chaos controlling of identical chemical reactor system via adaptive controlled hybrid projective synchronization

An investigation on microscopic chaos controlling of identical chemical reactor system via adaptive controlled hybrid projective synchronization

Controlling Chaos in a Newly Designed Chaotic Hamiltonian System Based on Hénon-Heiles Model using Active Controlled Hybrid Projective Synchronization

In this paper, a systematic approach is designed for investigating the hybrid projective synchronization (HPS) in identical chaotic Hamiltonian systems based on Hénon-Heiles Model by using active control method (ACM). Initially, an active control law is described to achieve asymptotic stability of state vectors of given system using Lyapunov stability theory (LST). Additionally, numerical simulations utilizing MATLAB toolbox are presented to validate the efficiency and effectiveness of the designed approach. Furthermore, the proposed strategy has numerous applications in encryption and secure communication.

Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters

<p style='text-indent:20px;'>This paper proposes a new scheme generalized hybrid projective synchronization for two different chaotic systems using adaptive control, where the master and slave systems do not necessarily have the same number of uncertain parameters. In this method the master system is synchronized by the sum of hybrid state variables for the slave system. Based on Lyapunov stability theory, an adaptive controller for the synchronization of two different chaotic systems is proposed, This method is also applicable if the master and slave systems are identical. As example the generalized hybrid projective synchronization between Vaidyanathan and Zeraoulia chaotic systems are discussed. Numerical simulation are provided to demonstrate the effectiveness of the proposed method.

Sliding Mode Disturbance Observer Control Based on Adaptive Hybrid Projective Compound Combination Synchronization in Fractional-Order Chaotic Systems

In this paper, the hybrid projective compound combination synchronization (HPCCS) in a class of commensurate fractional-order chaotic Genesio–Tesi system with unknown disturbance has been investigated. To deal with the problem of bounded disturbance, the nonlinear HPCCS is proposed for the fractional-order chaotic system. Further, by choosing the appropriate control gain parameters, the nonlinear fractional-order disturbance observer can approximate the disturbance efficiently. Based on the sliding mode control (SMC) method, a simple sliding mode surface has been introduced. Moreover, by using the Lyapunov stability theory, the designed adaptive SMC method establishes that the states of the three master and two chaotic slave systems are synchronized expeditiously. Finally, some numerical simulation results are illustrated to visualize the effectiveness and the utility of the developed approach on the considered system in the presence of the external unknown bounded disturbances using MATLAB.

Projective and hybrid projective synchronization of 4-D hyperchaotic system via nonlinear controller strategy

Nonlinear control strategy was established to realize the Projective Synchronization (PS) and Hybrid Projective Synchronization (HPS) for 4-D hyperchaotic system at different scaling matrices. This strategy, which is able to achieve projective and hybrid projective synchronization by more precise and adaptable method to provide a novel control scheme. On First stage, three scaling matrices were given in order to achieving various projective synchronization phenomena. While the HPS was implemented at specific scaling matrix in the second stage. Ultimately, the precision of controllers were compared and analyzed theoretically and numerically. The long-range precision of the proposed controllers are confirmed by third stage.

Hybrid Projective Synchronization of 4-D Hyperchaotic Systems via Adaptive Control

This paper designs a procedure for investigating the hybrid projective synchronization (HPS) scheme between two identical 4-D hyperchaotic systems. Based on Lyapunov stability theory (LST), an adaptive control technique (ACT) has been designed to achieve the desired HPS scheme. The suggested technique determines globally the asymptotic stability and identification of parameters simultaneously using HPS scheme. It is noted that complete , hybrid and anti-synchronization turns into particular cases of HPS scheme. Numerical simulations are presented to validate the effectivity and feasibleness of the considered technique by using MATLAB. Remarkably, the theoretical and computational outcomes are in complete agreement. Also, the considered HPS scheme is very efficient as it has numerous applications in encryption and secure communication.

Stability Analysis, Control of Simple Chaotic System and its Hybrid Projective Synchronization with Fractional Lu System

In this article, the stability analysis and chaos control of Simple chaotic system have been discussed. A new lemma based on Caputo derivative is used during the stability analysis of the fractional order Simple chaotic system through Lyapunov stability theory. During hybrid projective synchronization the Simple chaotic system is considered as drive system and Lu chaotic system is taken as response system. Nonlinear control method has been used to analyse the hybrid projective synchronization of fractional systems. For numerical simulations Adams-Bashforth-Moulton method has been used and results obtained are presented graphically.

Synchronization on the adaptive sliding mode controller for fractional order complex chaotic systems with uncertainty and disturbances

The present paper purports to examine and analyse the concept of non identical complex chaotic systems of fractional order with external bounded disturbances and uncertainties. Hybrid projective synchronization has been achieved between fractional order complex Lu-system (drive system) and complex T-system (slave system). The adaptive sliding mode control technique has been used to design control law through suitable sliding surface and estimate the uncertainties and external disturbances in order to establish the stability of controlled system by using allied theorems. Also we have compared our results with prior published literature results to determine the supremacy of considered methodology. Computer simulations outcomes have established the efficacy and adeptness of the prospective scheme.

Hybrid Projective Synchronization of Fractional-order Neural Networks with Different Dimensions

This paper is concerned with the problem of hybrid projective synchronization between two fractional-order neural networks with the order lying in the interval \((1,2)\). The coupled networks have ...

The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non-identical Dimensions and Orders.

This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings.

Stability of dynamical behavior of a new hyper chaotic system in certain range and its hybrid projective synchronization behavior

This article gives an insight for important tools to study the stability of dynamical behavior of newly constructed hyper chaotic systems within some certain parameter range. Further, hybrid projective synchronization (HPS) of two identical new hyper chaotic systems is defined and scheme of HPS is developed by using tracking control method. A new hyper chaotic system has been constructed and then response system. Numerical simulations verify the effectiveness of this scheme, which has been performed by mathematica and MATLAB.

Finite-time hybrid projective synchronization of the drive-response complex networks with distributed-delay via adaptive intermittent control

This paper studies the finite-time hybrid projective synchronization of the drive-response complex networks. In the model, general transmission delays and distributed delays are also considered. By designing the adaptive intermittent controllers, the response network can achieve hybrid projective synchronization with the drive system in finite time. Based on finite-time stability theory and several differential inequalities, some simple finite-time hybrid projective synchronization criteria are derived. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems

The topic related to the coexistence of different synchronization types between fractional-order chaotic systems is almost unexplored in the literature. Referring to commensurate and incommensurate fractional systems, this paper presents a new approach to rigorously study the coexistence of some synchronization types between nonidentical systems characterized by different dimensions and different orders. In particular, the paper shows that identical synchronization (IS), antiphase synchronization (AS), and inverse full state hybrid projective synchronization (IFSHPS) coexist when synchronizing a three-dimensional master system with a fourth-dimensional slave system. The approach, which can be applied to a wide class of chaotic/hyperchaotic fractional-order systems in the master-slave configuration, is based on two new theorems involving the fractional Lyapunov method and stability theory of linear fractional systems. Two examples are provided to highlight the capability of the conceived method. In particular, referring to commensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Rössler system of order 2.7 and the hyperchaotic four-dimensional Chen system of order 3.84. Finally, referring to incommensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Lü system of order 2.955 and the hyperchaotic four-dimensional Lorenz system of order 3.86.

A fractional-order form of a system with stable equilibria and its synchronization

There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is interesting that such a three-dimensional fractional system can exhibit chaotic attractors. Full-state hybrid projective synchronization scheme and inverse full-state hybrid projective synchronization scheme have been designed to synchronize the three-dimensional fractional system with different four-dimensional fractional systems. Numerical examples have verified the proposed synchronization schemes.

Hybrid projective synchronization between the fractional order systems

In this paper we have investigated Hybrid Projective Synchronization, between the fractional order chaotic systems of different dimensions. We have synchronized the fractional order chaotic Lü system, as a master system, with the fractional order hyperchaotic Rössler system as the slave system. Further, a fractional order hyperchaotic system is controlled by the fractional order chaotic financial system as the slave system. Numerical simulations are carried out using Matlab to show the effectiveness of the method.

Fractional order disturbance observer based adaptive sliding mode hybrid projective synchronization of fractional order Newton–Leipnik chaotic system

This manuscript, presents the fractional order disturbances observer based adaptive sliding mode hybrid projective synchronization of commensurate and incommensurate fractional order Newton–Leipnik chaotic system with disturbance. Firstly, a fractional order disturbance observer (FODO) based on adaptive sliding mode control laws for a fractional order Newton–Leipnik system with unknown bounded disturbance is studied. The appropriate control gain parameters are chosen such that the disturbance observer can approximate the unknown disturbance well. Further, we design a simple sliding mode surface based on sliding mode control technique incorporating with the designed fractional order disturbance observer for developing a bounded hybrid projective synchronization control scheme. Numerical simulation results are given to demonstrate the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. To analyse the superiority of proposed methodology we have compared our results with earlier published results as well. Moreover, as an application, the proposed scheme is then applied to a secure communication system. Simulation results verify the proposed schemes success in the communication application.