Synchronization of Chaotic Liouvillian Systems: An Application to Chua’s Oscillator

Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

“…Consider Chua's oscillator [ 25 ] with the following dimensionless equations where f ( x 1 ( t )) = m 1 x 1 ( t ) + (1/2)( m 0 − m 1 )(| x 1 ( t ) + 1| − | x 1 ( t ) − 1|), α , β , γ , m 0 , and m 1 are numbers. System ( 35 ) can be reformulated in the form of ( 1 ) with , , , , σ ( t ) = x 1 ( t ), and φ ( σ ( t )) = m 1 σ ( t ) + (1/2)( m 0 − m 1 )(| σ ( t ) + 1| − | σ ( t ) − 1|).…”

Colour image encryption via fractional chaotic state estimation

“…Fractional calculus has gained attention due to its many possible applications in various fields like finance [1], physics [2], medicine [3], biology [4], and chaotic systems synchronisation [5], this last one was first introduced by Pecora and Carroll [6] and since then, many possible uses to it were found.…”

Dynamic system with no equilibrium and its chaos anti-synchronization

“…The discovery of Lorenz has promoted the investigation of various chaotic systems [1][2][3][4][5][6]. Numerous studies have attempted to explain chaos synchronization [7][8][9][10]. Different schemes have been developed for synchronization of chaos, for example adaptive synchronization scheme [11], active control scheme [12], backstepping control [13], hybrid function synchronization [14], etc.…”