An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems

Chaos control and synchronization of the Φ6-Van der Pol system driven by external and parametric excitations

“…Nowadays, after the pioneering work of Pecora and Carrol [22], different techniques have been proposed to realize synchronization [25][26][27][28][29]. In this section, the chaos synchronization of 6 -Van der Pol oscillator with both external and parametric force is investigated by adaptive method.…”

Adaptive synchronization of uncertain hyperchaotic systems based on parameter identification

“…which has a hyperchaotic attractor when the positive system parameters are a = 0.25, b = 3, c = 0.5, d = 0.05 [12]. For convenience, we denoted the master Rö ssler hyperchaotic system in the form as in (1) _ The slave Rö ssler hyperchaotic system has the same structure as the master system but the system parameters are unknown, we denote it as…”

“…The sum of absolute value of synchronization errors: jx s (t) À x m (t)j + jy s (t) À y m (t)j + jz s (t) À z m (t)j + jw s (t) À w m (t)j. is full rank because det(b, Ab, A 2 b, A 3 b) = Àd 2 c + dca + dc 2 a À c À 2c 2 À c 3 5 0, where b = (0, 0, À1, 0) T . Therefore, from the control theory of linear system [17,18], the single-input dynamic system (12) is controllable, i.e., all the eigenvalues are controllable. Thus, we can select an appropriate feedback gain vector k such that system (11) is globally asymptotically stable at zero, that is dynamical system (10) is synchronous with Rö ssler hyper-chaotic system (5).…”

“…Recently, after the pioneering work of Pecora and Carrol in 1990 [1], synchronization phenomena in coupled chaotic systems have been extensively studied during the last decade due to its theoretical challenge and its great potential applications in secure communication, chemical reactions, biological systems and so on [2,3]. Great efforts have been devoted to achieving chaos synchronization in the last few years and a wide variety of approaches have been proposed, such as linear and nonlinear feedback synchronization methods [4,5], time-delay feedback synchronization methods [6], adaptive synchronization methods [7,8], impulsive synchronization methods [9], among many others (see [10][11][12][13][14] and references therein).…”

Synchronization control of cross-strict feedback hyperchaotic system based on cross active backstepping design

“…So hyperchaotic systems are typically implemented as a transmitter to improve the degree of security. Synchronization control of hyperchaotic systems is thus important in application, and different synchronization control methods have been investigated by Li [2], Elabbasy [3], Zhang [4,5], Park [6] and other researchers [7][8][9][10][11][12][13].…”