MODIFIED PROJECTIVE LAG SYNCHRONIZATION OF TWO NONIDENTICAL HYPERCHAOTIC COMPLEX NONLINEAR SYSTEMS

2011 ◽  
Vol 21 (08) ◽  
pp. 2369-2379 ◽  
Author(s):  
GAMAL M. MAHMOUD ◽  
EMAD E. MAHMOUD
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Active Control ◽  
Numerical Results ◽  
Control Technique ◽  
Lag Synchronization ◽  
Control Functions ◽  
Projective Lag Synchronization ◽  
Complex Nonlinear Systems ◽  
Analytical Expressions

In this work, we introduce and investigate the modified projective lag synchronization (MPLS) of two nonidentical hyperchaotic complex nonlinear systems. The idea of an active control technique based on complex Lyapunov function with lag in time is used for an approach to investigate MPLS of hyperchaotic attractors of these systems. For illustration, this approach is applied to hyperchaotic complex Chen and Lü systems. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve MPLS.

Complex lag synchronization of two identical chaotic complex nonlinear systems

Open Physics ◽  
2014 ◽  
Vol 12 (1) ◽  
Author(s):  
Emad Mahmoud ◽  
Kholod Abualnaja
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Chaotic Attractors ◽  
State Variables ◽  
Lag Synchronization ◽  
Phase Errors ◽  
New Type ◽  
Complex Nonlinear Systems ◽  
Definition Of ◽  
Made In

AbstractMuch progress has been made in the research of synchronization for chaotic real or complex nonlinear systems. In this paper we introduce a new type of synchronization which can be studied only for chaotic complex nonlinear systems. This type of synchronization may be called complex lag synchronization (CLS). A definition of CLS is introduced and investigated for two identical chaotic complex nonlinear systems. Based on Lyapunov function a scheme is designed to achieve CLS of chaotic attractors of these systems. The effectiveness of the obtained results is illustrated by a simulation example. Numerical results are plotted to show state variables, modulus errors and phase errors of these chaotic attractors after synchronization to prove that CLS is achieved.

AN ACTIVE CONTROL FOR CHAOS SYNCHRONIZATION OF REAL AND COMPLEX VAN DER POL OSCILLATORS

2007 ◽  
Vol 18 (05) ◽  
pp. 795-804 ◽  
Author(s):  
AHMED A. M. FARGHALY
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Active Control ◽  
Limit Cycles ◽  
Chaos Synchronization ◽  
Control Technique ◽  
Control Input ◽  
Van Der Pol ◽  
Van Der Pol Oscillators

In a recent paper [Chaos, Solitons Fractals21, 915 (2004)], both real and complex Van der Pol oscillators were introduced and shown to exhibit chaotic limit cycles. In the present work these oscillators are synchronized by applying an active control technique. Based on Lyapunov function, the control input vectors are chosen and activated to achieve synchronization. The feasibility and effectiveness of the proposed technique are verified through numerical simulations.

Lag synchronization of hyperchaotic complex nonlinear systems

2011 ◽  
Vol 67 (2) ◽  
pp. 1613-1622 ◽  
Author(s):  
Gamal M. Mahmoud ◽  
Emad E. Mahmoud
Keyword(s):  
Nonlinear Systems ◽  
Lag Synchronization ◽  
Complex Nonlinear Systems

scholarly journals Analytical and Numerical Study of the Projective Synchronization of the Chaotic Complex Nonlinear Systems with Uncertain Parameters and Its Applications in Secure Communication

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kholod M. Abualnaja ◽  
Emad E. Mahmoud
Keyword(s):  
Applied Sciences ◽  
Nonlinear Systems ◽  
Secure Communication ◽  
Numerical Study ◽  
Projective Synchronization ◽  
Control Technique ◽  
Uncertain Parameters ◽  
Complex Nonlinear Systems ◽  
Synchronization Scheme ◽  
Theoretical Results

The main aim of this research is to find an analytical and numerical study to investigate the projective synchronization of two identical or nonidentical chaotic complex nonlinear systems with uncertain parameters. The secure communication between these systems is achieved based on this study. Based on the adaptive control technique and the Lyapunov function a scheme is designed to achieve projective synchronization of chaotic attractors of these systems. The projective synchronization of two identical complex Chen systems and two different chaotic complex Lü and Lorenz systems is taken as two examples to verify the feasibility of the presented scheme. These chaotic complex systems appear in several applications in physics, engineering, and other applied sciences. Numerical simulations are calculated to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results. The above results will provide theoretical foundation for the secure communication applications based on the proposed scheme.

Active Control Technique Evaluation for Spacecraft (ACES)

1988 ◽  
Author(s):  
R. D. Irwin ◽  
Victoria Jones ◽  
Sally C. Rice ◽  
Sherman M. Seltzer ◽  
Danny K. Tollison
Keyword(s):  
Active Control ◽  
Control Technique ◽  
Technique Evaluation

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

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