Modified projective and modified function projective synchronization of a class of real nonlinear systems and a class of complex nonlinear systems

Sun, Junwei; Shen, Yi; Zhang, Xuncai

doi:10.1007/s11071-014-1558-z

Cited by 30 publications

(24 citation statements)

References 38 publications

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“…In this subsection, the chaotic Lorenz system is taken as one of the two real drive systems, described by (25) where x = (x 1 , x 2 , x 3 ) T is a real state vector, A = (a 1 , a 2 , a 3 ) T is a real vector of unknown parameters, and…”

Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

“…According to the theorem 1 in section II, AGCCS controller and parameter update laws for the systems (25), (26) and (27), can be designed in the form of…”

Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

“…The true values of unknown parameters are set as A = (10, 28, 8/3) T , B = (35, 28, 3) T and C = (45, 25, 6, 5) T , respectively, which can ensure that the drive systems (25) and (26) operate chaotically, and the response system (27) operates in hyperchaotic state without control. The initial conditions of the systems (25), (26) and (27) are arbitrarily chosen as x(0) = (−10, 0, 37) T , y(0) = (5, −14, −16) T and z(0) = (3.6 − 0.6 j, 0.9 − j, 13, 15) T , separately.…”

Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

“…1 shows the 3D phase portraits of the response system (27) before and after synchronization, respectively. When the AGCCS controller is activated, the response system (27) changes its original behavior according to the drive systems (25) and (26) with respect to the given complex mapping vectors (28). The AGCCS errors between the drive systems (25), (26) and response system (27) (25), (26) and (27) are drawn in Figs.…”

Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

“…23 As introduced in Refs. [24][25][26][27][28], synchronization between chaotic real and complex systems can offer more options of chaotic generators for secure communication and digital cryptography, which can increase the difficulty to decrypt and decipher the encrypted signals and information. Hence, it is meaningful and challenging to explore various synchronization schemes of nonlinear real and complex systems.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems

Wang

et al. 2016

AIP Advances

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With comprehensive consideration of generalized synchronization, combination synchronization and adaptive control, this paper investigates a novel adaptive generalized combination complex synchronization (AGCCS) scheme for different real and complex nonlinear systems with unknown parameters. On the basis of Lyapunov stability theory and adaptive control, an AGCCS controller and parameter update laws are derived to achieve synchronization and parameter identification of two real drive systems and a complex response system, as well as two complex drive systems and a real response system. Two simulation examples, namely, ACGCS for chaotic real Lorenz and Chen systems driving a hyperchaotic complex Lü system, and hyperchaotic complex Lorenz and Chen systems driving a real chaotic Lü system, are presented to verify the feasibility and effectiveness of the proposed scheme.

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Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

“…According to the theorem 1 in section II, AGCCS controller and parameter update laws for the systems (25), (26) and (27), can be designed in the form of…”

Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

Section: A Agccs Of Two Chaotic Real Drive Systems and One Hyperchaomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems

Wang

et al. 2016

AIP Advances

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Hybrid control of synchronization of fractional order nonlinear systems

Mohadeszadeh

Pariz

2019

Asian Journal of Control

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Under the existence of model uncertainties and external disturbance, finite‐time projective synchronization between two identical complex and two identical real fractional‐order (FO) chaotic systems are achieved by employing FO sliding mode control approach. In this paper, to ensure the occurrence of synchronization and asymptotic stability of the proposed methods, a sliding surface is designed and the Lyapunov direct method is used. By using integer and FO derivatives of a Lyapunov function, three different FO real and complex control laws are derived. A hybrid controller based on a switching law is designed. Its behavior is more efficient that if the individual controllers were designed based on the minimization of an appropriate cost function. Numerical simulations are implemented for verifying the effectiveness of the methods.

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A novel dual memristor hyperchaotic system and its application for secure communication based on three‐fold function projection synchronization

Jiang

Deng

et al. 2020

Int J Numerical Modelling

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A novel simplest four‐dimensional hyperchaotic system with dual memristors is designed by using a charge‐controlled memristor and a generalized voltage‐controlled memristor. Based on the conventional dynamic analysis method and MATLAB simulation software, the dynamic characteristics of the dual memristor hyperchaotic system such as Lyapunov exponent spectrum, phase diagram, and bifurcation diagram are studied. The novel system is found to exhibit singular nonlinear phenomena, such as limit cycle, state transition and multiple scroll attractor with certain parameter values. Being different from most known chaotic systems, which contain only two isolated unstable equilibrium points, the novel system has an infinite number of unstable equilibriums points and a larger Lyapunov exponent. What is more, the three‐fold function projection synchronization of the dual memristor hyperchaotic system and its application for secure communication is studied. Based on Lyapunov stabilization theory and adaptive sliding mode control method, three driving systems and three response systems are synchronized according to the corresponding scaling function matrix, respectively. In the secure communication system, the message signal is separated into three parts loaded in the different drive systems with different initial conditions to increase the reliability. The corresponding numerical simulations demonstrate the effectiveness of the results obtained.

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Modified projective and modified function projective synchronization of a class of real nonlinear systems and a class of complex nonlinear systems

Cited by 30 publications

References 38 publications

Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems

Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems

Hybrid control of synchronization of fractional order nonlinear systems

A novel dual memristor hyperchaotic system and its application for secure communication based on three‐fold function projection synchronization

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