Projective synchronization for coupled partially linear complex‐variable systems with known parameters

Abstract

The passivity theory is used to achieve projective synchronization in coupled partially linear complex‐variable systems with known parameters. By using this theory, the control law is thus adopted to make state vectors asymptotically synchronized up to a desired scaling factor. This paper deals with sending different large messages which include image and voice signals. The theoretical foundation of the projective synchronization based on the passivity theory is exploited for application to secure communications. The numerical simulations of secure communication are used to send large message, an image and sound (voice) signal. The errors are controlled to zero that show the agreement between theoretical and numerical simulations results. Copyright © 2016 John Wiley & Sons, Ltd.

Complex anti-synchronization of two indistinguishable chaotic complex nonlinear models

“…It is straightforward and accommodating to use this plan for chaos and hyperchaos complex structures. We apply our method, for example, for two vague wild, complicated systems with different beginning characteristics the fundamental structure (16) and slave frameworks (17). Numerical entertainments of our case affirm all the theoretical results.…”

“…In Figure 1, the arrangements of equations (16) and (17) are proposed subject to different starting states and show that CAS is achieved after a by no time t. We can see that each u 1s , u 3s have a similar indication of u 2m , u 4m while u 2s , u 4s have an inverse indication of u 1m , u 3m . This implies CS accomplishes between the imaginary element of model (16) and the real element of model (17) while AS happens between the real part of slave structure (16) and the imaginary part of the main structure (17). It is evident from Figure 1 that the state variable of the main system synchronizes with a different state variable of the slave system.…”

“…To manifest and assert the handiness of the suggested design, we light up the reproduction aftereffects of the CAS amid two same chaos complex systems (16) and (17). Structures (16) and (17) with the controller (20) are lighted numerically. The parameters of the framework (16) are picked as a = 30, b = 14, c = 1 and d = 2, where the chaotic behavior is obtained.…”

“…CAS between two indistinguishable frameworks(16) and(17)with the controller(19): (a) u 1m and u 2s vary t, (b) u 2m and u 1s vary t, (c) u 3m and u 4s vary t and (d) u 4m and u 3s vary t.…”

Fractional matrix and inverse matrix projective synchronization methods for synchronizing the disturbed fractional‐order hyperchaotic system

“…Since the introduction of the synchronization for two chaotic signals starting at different initial conditions, more and more attention has been devoted to the control and synchronization for the chaotic and fractional‐order chaotic systems. Moreover, the types of synchronization are extended to complete synchronization, antisynchronization, phase synchronization, generalized synchronization, projective synchronization, and so on. In order to achieve these synchronizations, various synchronization methods such as linear and nonlinear feedback control, active control, adaptive control, sliding‐mode control, and backstepping design technique have been successfully used for the chaotic and fractional‐order chaotic systems.…”