Temporary lag and anticipated synchronization and anti-synchronization of uncoupled time-delayed chaotic systems

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

“…Nowadays, more and more techniques of chaos synchronization were proposed, such as active control [2][3][4], backstepping control method [5][6][7][8], linear error feedback control [9][10][11], adaptive control [12][13][14][15][16], and sliding mode control [17][18][19][20].…”

“…It means these states are always in the first quadrant, such as the three species prey-predator systems [15,16,21], double Mackey-Glass systems [17,22,23], energy communication system in biological research [19,24], and virus-immune system [20]. For the three species preypredator systems, which consist of two competing preys and one predator can be described by the following set of nonlinear differential equations: = 1, 2 represent the densities of the two prey species and represents the density of the predator species.…”

Generalized projective synchronization of chaotic satellites problem using linear matrix inequality

“…Synchronization phenomena in chaotic systems have attracted much attention since the work of pecora and carroll [11]. Up to now, various types of synchronization phenomena are being reported for chaotic systems, such as complete synchronization (CS) [12], phase synchronization (PS) [13], anti-phase synchronization (APS) [14], lag synchronization (LS) [15], and generalized synchronization (GS) [16], and projective function synchronization [17].…”

Complex Projective Synchronization in Drive-Response Stochastic Complex Networks by Impulsive Pinning Control

“…Up to now, the investigation on the synchronization of complex networks has attracted a great deal of attentions due to its potential applications in various fields, such as physics, secure communication, automatic control, biology, and sociology [1][2][3][4][5]. In literature, there are many widely studied synchronization patterns, which define the correlated in-time behaviors among the nodes in a dynamical network, for example, complete synchronization [6][7][8], phase synchronization [9,10], lag synchronization [11][12][13], antisynchronization [14][15][16], projective synchronization [17][18][19][20][21][22][23][24][25][26][27][28][29], and so on. Projective synchronization reflects a kind of proportionality between the synchronized states, so it is an interesting research topic and has many applications.…”

“…Besides, due to the finite information transmission and processing speeds among the units, the connection delays in realistic modeling of many large networks with communication must be taken into account, such as [19,23,24,35]. What is more, uncertainties commonly exist in the real world, such as stochastic forces on the physical systems and noisy measurements caused by environmental uncertainties; the stochastic forms from the same noise of one-dimensional vector to the different noise perturbations of vector were investigated in [9,10,15,17,25]. Therefore, it is important to study the effect of time delay and stochastic noise in complex projective synchronization of drive-response networks.…”