Journal of Applied Nonlinear Dynamics
Nonlinear Control Technique for Dual Combination Synchronization of Complex Chaotic Systems
Journal of Environmental Accounting and Management 8(2) (2019) 261277  DOI:10.5890/JAND.2019.06.009
Ajit K. Singh$^{1}$, Vijay K. Yadav$^{2}$, S. Das$^{2}$
$^{1}$ Department of Mathematics, National Institute of Technology, Hamirpur, HP 177005, India
$^{2}$ Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi  221005, India
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Abstract
In this article, the authors have investigated a novel scheme of dual combination synchronization among six different complex chaotic systems using nonlinear control technique. The important feature of the considered dual combination synchronization is various synchronization processes viz., complete synchronization, combination synchronization, projective synchronization, dual synchronization, chaos control problem become particular cases of the said scheme. Since complex chaotic systems have additional variables and complexity in behaviours, the scheme is expected to be more secure for transmitting and receiving signals in communication theory. The stability analysisof the scheme is achieved by using nonlinear control method based on Lyapunov stability theory. The corresponding theoretical results are being simulated using fourth order RungeKutta algorithm taking complex Lorenz system, complex Lu system, complex T system, complex Chen system as drive systems and complex two coupled dynamos system and a new nonlinear complex chaotic system as response systems. The results are depicted through graphical presentations for different particular cases.
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