Function projective synchronization of identical and non-identical modified finance and Shimizu–Morioka systems

Kareem, S.O.; Ojo, K. S.; Njah, A. N.

doi:10.1007/s12043-012-0281-x

Cited by 18 publications

(11 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerical solutions are now presented to verify the effectiveness of controllers (24) and (30)- (34). In all six cases presented, the periodically driven oscillator parameters selected remain constant at = 100, = 300, = 0.35, = 0.2, = 1.0, 0 = 1.51, and = 10.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…These methods include adaptive control [33], active control [34], sliding mode control [35], impulsive control [36], linear feedback control [37], backstepping control [38], open plus close loop control [39], adaptive fuzzy feedback [40], and passive control [41]. Notable among this method is the backstepping control technique which has outstanding performance in the synchronization of identical and nonidentical chaotic systems [42,43].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiswitching Synchronization of a Driven Hyperchaotic Circuit Using Active Backstepping

Ajayi

Ojo

Vincent

et al. 2014

Journal of Nonlinear Dynamics

View full text Add to dashboard Cite

An active backstepping technique is proposed for the realization of multiswitching synchronization of periodically forced hyperchaotic Van der Pol-Duffing oscillators. The active backstepping technique is a systematic design approach with recursive procedures that skillfully optimizes the choice of Lyapunov functions and active control technique. Using the active backstepping technique, the usual master-slave synchronization scheme is extended to study the synchronization of systems with different combinations of the slave states variables with master state variables. Our numerical results confirm the effectiveness of the proposed analytical technique.

show abstract

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiswitching Synchronization of a Driven Hyperchaotic Circuit Using Active Backstepping

Ajayi

Ojo

Vincent

et al. 2014

Journal of Nonlinear Dynamics

View full text Add to dashboard Cite

show abstract

“…Also, in 1990 Ott et al 12 introduced the OGY method for controlling chaos. Looking for better techniques for chaos control and synchronization distinctive sorts of strategies have been created for controlling chaos and synchronization of nonidentical and identical systems for instance linear feedback, 13 optimal control, 14 adaptive control, 15 active control, 16 sliding control, 17 backstepping control, 18 robust adaptive sliding mode control, 19 etc. In the published literature, it is vital to know the values of system's parameters for the derivation of the controller.…”

Section: Introductionmentioning

confidence: 99%

Generalization of combination‐combination synchronization of n‐dimensional time‐delay chaotic system via robust adaptive sliding mode control

Khan

Singh

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

In this manuscript, the methodology to achieve combination-combination synchronization of time-delay chaotic system via robust adaptive sliding mode control is introduced. The methodology is implemented by taking identical multiple time-delay Lorenz chaotic system. By using rigorous mathematical theory, the sufficient condition is drawn for the stability of error dynamics based on Lyapunov stability theory. Theoretical results are supported with the numerical simulations.

show abstract

“…For example, an active-control technique has been provided for the identical and non-identical synchronisation of fractional-order chaotic systems (Srivastava et al, 2014). In a different application, function-projective synchronisations (FPS) of identical and non-identical modified finance systems (MFS) and the Shimizu-Morioka system (S-MS) have been studied via active control technique (Kareem et al, 2012). Fast projective synchronisation of fractional-order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB) have also been reviewed (Muthukumar PROCEEDINGS OF THE LATVIAN ACADEMY OF SCIENCES.…”

mentioning

confidence: 99%

Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Noghredani

Balochian

2017

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

View full text Add to dashboard Cite

INTRODUCTIONThe broad field of chaos theory has been among the most interesting issues researchers have studied in recent decades. Concepts related to chaos theory and its related disciplines are employed in different fields, including medicine (Sarbaz et al., 2012;Aghababa and Borjkhani 2014;Provata et al., 2012), economics (Pan et al., 2012;Airaudo and Zanna, 2012), functioning of laser diodes (Banerjee et al., 2012;Gao, 2012), and mathematics (Hosseinalipour, 2013;Kupka, 2014). The control of chaos-related phenomena has attracted wide attention from many different kinds of researchers.Although the idea of fractional-order operators has a history as long as that of integer-order operators, interest in this field is expanding due to an increasing amount of attention from scientists and mathematicians. In recent decades, fractional-order operators have been the driving force behind an increasing number of investigations. With the development of studies in this area, practical and theoretical investigations into the application of fractional-order operators in engineering sciences have now become widespread in the academic community (Padula and Visioli, 2014;Pakzad et al., 2013;Tripathy et al., 2015a;Tripathy et al., 2015b). For example, fractional-order calculations have been applied in mechanical and electrical engineering, biology, economics, and mathematics, among other fields (Hernandez et al., 2014;Wang and Li, 2014;Cortes and Elejabarrieta, 2007).A chaotic system is a highly complex, dynamic nonlinear system. The important and salient characteristics of chaotic systems include their extreme sensitivity to initial conditions, making the synchronisation of chaotic systems vital. The rapid increase in interest in fractional-order chaotic systems has manifested in investigations into the chaotic behavior of fractional-order horizontal platform systems (Aghababa, 2014) and in the proliferation of other published articles on these systems (Yin et al., 2013;Li and Chen, 2014;Li and Tong, 2013).During the past two decades, the control and synchronisation of fractional-order and integer-order chaotic systems have largely attracted scientists and researchers due to their potential applications in secure communications, biological systems, medicine, and other fields. For example, an active-control technique has been provided for the identical and non-identical synchronisation of fractional-order chaotic systems (Srivastava et al., 2014). In a different application, function-projective synchronisations (FPS) of identical and non-identical modified finance systems (MFS) and the Shimizu-Morioka system (S-MS) have been studied via active control technique (Kareem et al., 2012). Fast projective synchronisation of fractional-order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB) have also been reviewed (Muthukumar PROCEEDINGS OF THE LATVIAN ACADEMY OF SCIENCES. Section B, Vol. 71 (2017)

show abstract

Function projective synchronization of identical and non-identical modified finance and Shimizu–Morioka systems

Cited by 18 publications

References 19 publications

Multiswitching Synchronization of a Driven Hyperchaotic Circuit Using Active Backstepping

Multiswitching Synchronization of a Driven Hyperchaotic Circuit Using Active Backstepping

Generalization of combination‐combination synchronization of n‐dimensional time‐delay chaotic system via robust adaptive sliding mode control

Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Contact Info

Product

Resources

About