Synchronization and an application of a novel fractional order King Cobra chaotic system

Abstract

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.

Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

“…If K > 0 and s > 0, then the state trajectories of the fractional-order error dynamical system (23) will converge to the sliding surface s = 0. That is, the synchronization between the fractional order dynamical systems (8) and (9) is globally asymptotically stable.…”

“…X, Y ∈ R n are the state variables, A, B ∈ R n×n are the coefficient of the linear parts, and F, G are nonlinear parts such that F, G : R n → R n of the systems (8) and (9), respectively. U (X, Y ) is the control input to be determined later.…”

“…Proof Consider the fractional-order error dynamical system (23) In (23), A is a coefficient matrix of linear parts of the fractional-order system (8), and C and M are parameter matrices whose entries are in the real line. Hence, the fractional order error dynamical system (23) has no nonlinear terms.…”

“…Synchronization of fractional-order chaotic systems is increasing interest among researchers in the past few years. Also, it has been growing continuously due to its potential applications in cryptography or secure communication, signal and control processing [3][4][5][6][7][8]. Latterly, several techniques and methods have been improved and applied for chaos control and synchronization.…”

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

“…[22][23][24][25][26][27][28][29], and it has been a popular research area. Recently, a number of control schemes have been developed to achieve various synchronization of memristor-based systems and complex systems.…”