Self-Excited and Hidden Attractors in an Autonomous Josephson Jerk Oscillator: Analysis and Its Application to Text Encryption

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Sifeu Takougang Kingni ◽  
Gaetan Fautso Kuiate ◽  
Victor Kamdoum Tamba ◽  
Viet-Thanh Pham ◽  
Duy Vo Hoang
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Projective Synchronization ◽  
Chaotic Attractors ◽  
Generalized Function ◽  
Function Projective Synchronization ◽  
Dc Bias ◽  
The Stability ◽  
Security Device ◽  
High Level

By converting the resistive capacitive shunted junction model to a jerk oscillator, an autonomous chaotic Josephson jerk oscillator which can belong to oscillators with hidden and self-excited attractors is designed. The proposed autonomous Josephson jerk oscillator has two or no equilibrium points depending on DC bias current. The stability analysis of the two equilibrium points shows that one of the equilibrium points is unstable while for the other equilibrium point, the existence of a Hopf bifurcation is established. The dynamical behavior of autonomous Josephson jerk oscillator is analyzed by using standard tools of nonlinear analysis. For a suitable choice of the parameters, an autonomous Josephson jerk oscillator can generate antimonotonicity, periodic oscillations, self-excited chaotic attractors, hidden chaotic attractors, hidden chaotic bubble attractors, and coexistence between periodic and chaotic self-excited attractors. Finally, a text cryptographic encryption scheme with the help of generalized function projective synchronization of the proposed autonomous Josephson jerk oscillators in hidden chaotic attractor regime is illustrated through a numerical example, showing that a high-level security device can be produced using this system.

scholarly journals Compound Generalized Function Projective Synchronization for Fractional-Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Chunde Yang ◽  
Hao Cai ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Drive System ◽  
Projective Synchronization ◽  
Order System ◽  
Generalized Function ◽  
Function Projective Synchronization ◽  
The Stability ◽  
Generalized Function Projective Synchronization

A modified function projective synchronization for fractional-order chaotic system, called compound generalized function projective synchronization (CGFPS), is proposed theoretically in this paper. There are one scaling-drive system, more than one base-drive system, and one response system in the scheme of CGFPS, and the scaling function matrices come from multidrive systems. The proposed CGFPS technique is based on the stability theory of fractional-order system. Moreover, we achieve the CGFPS between three-driver chaotic systems, that is, the fractional-order Arneodo chaotic system, the fractional-order Chen chaotic system, and the fractional-order Lu chaotic system, and one response chaotic system, that is, the fractional-order Lorenz chaotic system. Numerical experiments are demonstrated to verify the effectiveness of the CGFPS scheme.

Chaos Synchronization of the Modified Sprott E System

2013 ◽  
Vol 798-799 ◽  
pp. 672-675
Author(s):  
Xiao Ya Yang
Keyword(s):  
Numerical Simulation ◽  
Chaos Synchronization ◽  
Dynamical Behavior ◽  
Global Bifurcation ◽  
Projective Synchronization ◽  
Chaotic Attractors ◽  
Full State ◽  
Hybrid Projective Synchronization

In this paper, chaos synchronization of the modified Sprott E system is investigated. Firstly, the chaotic attractors on different phase planes of the system are got by means of numerical simulation. When , the abundance dynamical behavior of the system is presented by the global bifurcation graph. Then, the chaos synchronization of the system by the full state hybrid projective synchronization (FSHPS) method is realized.

SYMMETRY BREAKING BIFURCATIONS OF CHAOTIC ATTRACTORS

1995 ◽  
Vol 05 (06) ◽  
pp. 1643-1676 ◽  
Author(s):  
PHILIP J. ASTON ◽  
MICHAEL DELLNITZ
Keyword(s):  
Lyapunov Exponent ◽  
Symmetry Breaking ◽  
Coupled Oscillators ◽  
Dynamical Behavior ◽  
Invariant Sets ◽  
Chaotic Attractors ◽  
Loss Of Stability ◽  
Efficient Computation ◽  
The Stability

In an array of coupled oscillators, synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries, and this leads to the idea of symmetry breaking bifurcations of chaotic attractors. Finally, the results and ideas are illustrated for several systems of coupled oscillators.

scholarly journals Multifarious Chaotic Attractors and Its Control in Rigid Body Attitude Dynamical System

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yang Wang ◽  
Zhen Wang ◽  
Dezhi Kong ◽  
Lingyun Kong ◽  
Yukun Qiao
Keyword(s):  
Rigid Body ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Euler Angle ◽  
Chaotic Attractors ◽  
Attitude Motion ◽  
Control Law ◽  
Relay Control ◽  
Body Attitude ◽  
The Stability

The Euler dynamical equation which describes the attitude motion of a rigid body will exhibit very complex dynamic behaviors under the action of different external torques. Many special types of new chaotic attractors are presented, including hidden attractors, double-body-double-core chaotic attractors, and single-body-three-core-tree-wing chaotic attractors. The position of equilibrium points in several typical cases of the Euler dynamic equation is solved, and the stability of linearized equation at each equilibrium point and its influence on the formation of the chaotic attractor are analyzed. An improved nonlinear relay control law based on Euler angle feedback is developed to stabilize a new chaotic spacecraft attitude motion to an appointed equilibrium point or a periodic orbit.

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