Combination–combination phase synchronization among non-identical fractional order complex chaotic systems via nonlinear control

Yadav, Vijay K.; Prasad, Ghanshyam; Srivastava, Mayank; Das, S.

doi:10.1007/s40435-018-0432-0

Cited by 16 publications

(21 citation statements)

References 41 publications

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“…There could be many possible switching combinations for the three master systems (9) (10), ( 11) and one response system (12) and out of that we selected randomly few of them which are given below.…”

Section: Multi-switching Compound Synchronization With Uncertain Parameters and External Disturbancementioning

confidence: 99%

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Multi-switching Compound Synchronization of Different Chaotic Systems with External Disturbances and Parametric Uncertainties via Two Approaches

Shukla¹,

Vishal

Srivastava³

et al. 2021

Int. J. Appl. Comput. Math

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This article deals with the multi-switching compound synchronization (MSCS) between four different chaotic systems with parametric uncertainties and external disturbances. Based on two analytical approaches viz. Lyapunov's second method and Cardano's method, the MSCS of three different uncertain chaotic systems (drive systems) and one uncertain chaotic system (response system) is examined. Theoretical and numerical results describe that the projected method is consistent and easy to execute for MSCS.

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Section: Multi-switching Compound Synchronization With Uncertain Parameters and External Disturbancementioning

confidence: 99%

“…Pecora and Carroll [2] also gave the idea of control of chaotic drive and developed the concept of conditional Lyapunov exponents. After this, many types of different synchronization have studied by several researchers [3][4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Multi-switching Compound Synchronization of Different Chaotic Systems with External Disturbances and Parametric Uncertainties via Two Approaches

Shukla¹,

Vishal

Srivastava³

et al. 2021

Int. J. Appl. Comput. Math

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“…Also in Ref. [48], author discussed phase synchronization between different complex chaotic systems of fractional order, by this procedure, the C-C synchronization has been carried out at t = 4.5 (approx.). Furthermore, in Ref.…”

Section: Casementioning

confidence: 99%

“…Further, C-C phase synchronization between different fractional order complex nonlinear chaotic systems via active control is studied in Ref. [48]. Also, finite-time combination synchronization among three non-identical chaotic systems is discussed in Ref.…”

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confidence: 99%

Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

Khan

Chaudhary

2020

Arab. J. Math.

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In this paper, we investigate a hybrid projective combination-combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination-combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB. Mathematics Subject Classification 34K23 • 34K35 • 37B25 • 37N35 1 Introduction Chaos is described as a nonlinear extremely complex phenomenon found in nature featuring the high sensitivity to the initial conditions. These features are defined as butterfly effect, the term coined by Lorenz in 1963. Chaos theory is widely applicable to various fields of applied sciences and engineering, for instance, secure communication [1], biomedical engineering [2], machine learning, circuits [3], finance models [4], jerk systems [5], weather models [6], neural networks [7], oscillations [8], robotics [9], chemical reactions [10], encryption [11], ecological models [12], etc. Consequently, chaos theory has become one of the most appealing fields for researchers and engineers in recent times. Historically, chaos theory dates back to the remarkable work of Poincare [13] established in 1890s while dealing with three-body problem to stabilize the solar system. In fact, he advocated the qualitatively behaviour, using geometric quantitatively to display the universal configuration of all solutions. Despite the observations made by Poincare [13], the first formal introduction of chaos in a deterministic system was proposed by Lorenz [14]. Lorenz observed that simple meteorological models depicted sensitive dependence on the initial conditions, known as butterfly effect, which established that chaos theory is widely applicable in other interdisciplinary areas also. Though the fundamental work on chaos synchronization had been carried by [15], the rapid growth in the field was seen after the phenomenal work of Ott et al. [16]. However, the concept of chaos synchronization was first introduced by Pecora and Carroll [17], wherein they performed synchronization of two identical chaotic systems based on master-slave composition which was unknown for the past 3 decades. Later on, many researchers carried forward the pioneered work of Pecora and Carroll and it has been established that chaos synchronization is also achievable for non-identical chaotic systems possessing absolutely different initial conditions.

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“…Naval Laboratory put forward the master-slave chaotic synchronization scheme, which realized the synchronization of two chaotic systems in the circuit and promoted the theoretical study of chaotic synchronization and chaotic control [24]. So far, there are many types of synchronization, such as complete synchronization [25][26][27], antisynchronization [28], lag synchronization [29,30], generalized synchronization [31], projective synchronization [32][33][34][35], and phase and antiphase synchronization [36]. The scale factor of projective synchronization can be set flexibly, which enhances the uncertainty of slave system and improves communication security.…”

Section: Introductionmentioning

confidence: 99%

Projective Synchronization of Nonidentical Fractional-Order Memristive Neural Networks

Chen

Ding

2019

Discrete Dynamics in Nature and Society

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This paper investigates projective synchronization of nonidentical fractional-order memristive neural networks (NFMNN) via sliding mode controller. Firstly, based on the sliding mode control theory, a new fractional-order integral sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, according to fractional-order differential inequalities and fractional-order Lyapunov direct method, the trajectories of the system converge to the sliding mode surface to carry out sliding mode motion, and some sufficient criteria are obtained to achieve global projective synchronization of NFMNN. In addition, the conclusions extend and improve some previous works on the synchronization of fractional-order memristive neural networks (FMNN). Finally, a simulation example is given to verify the effectiveness and correctness of the obtained results.

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Combination–combination phase synchronization among non-identical fractional order complex chaotic systems via nonlinear control

Cited by 16 publications

References 41 publications

Multi-switching Compound Synchronization of Different Chaotic Systems with External Disturbances and Parametric Uncertainties via Two Approaches

Multi-switching Compound Synchronization of Different Chaotic Systems with External Disturbances and Parametric Uncertainties via Two Approaches

Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

Projective Synchronization of Nonidentical Fractional-Order Memristive Neural Networks

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