Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms

Mahmoud, Emad E.; Al-Adwani, Madeha A.

doi:10.1016/j.rinp.2017.02.039

Cited by 25 publications

(14 citation statements)

References 24 publications

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“…Thus, by comparing the quaternion systems (34) and (35) with the form of systems (21) and (22), respectively, we find that…”

Section: Examplementioning

confidence: 99%

“…The chaotic complex Lorenz system (2) is therefore described by a five-dimensional (5D) system of real first-order autonomous ordinary differential equations. The physics of detuned lasers and the thermal convection of liquid flows are described and simulated via the complex Lorenz equations [21], where the complex variables are used to represent the electric field and the atomic polarization amplitude.In addition, one interesting possibility of the study of complex systems is that of modelling biological systems such as humans. For example, nonlinear systems have been used to characterize the human (see for example [22] and the references cited there).…”

Section: Introductionmentioning

confidence: 99%

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A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Application

2019

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In this paper, a chaotic quaternion autonomous nonlinear structure is introduced and intends to be a contribution. It is the first nonlinear dynamical system with quaternion variables to be studied in the literature. With nine dimensions, the new system is a high-dimensional one. Several vital characteristics and features of this model are investigated, such as its Hamiltonian, symmetry, signal flow graph, dissipation, equilibriums and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams, and chaotic behavior. A circuit implementation is designed to realize the new system, and a scheme is designed to achieve anti-anticipating synchronization (AAS) of two identical chaotic attractors with quaternion variables based on a Lyapunov function and active control. The concept of AAS is yet to be explored in the literature. A simulation experiment is designed and executed to illustrate the effectiveness of the acquired results. After synchronization, numerical outcomes are planned to explain the status variables and errors of these chaotic attractors to prove that AAS is achieved. The secure communication problem is studied based on the obtained events of the AAS of two identical nonlinear Lorenz systems with quaternion variables. AAS connecting the drive and response systems in chaotic systems with quaternion variables is the key to achieving communication. Signal encryption and restoration are simulated numerically.

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“…Thus, by comparing the quaternion systems (34) and (35) with the form of systems (21) and (22), respectively, we find that…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Application

2019

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“…A bifurcation diagram outlines a system parameter on the horizontal axis and a report of the attractor's action on the vertical axis. So, bifurcation diagrams present a kind method to picture how a system's behavior varies according to the value of a parameter [33]. Figure 2 shows ( , 5 ) bifurcation diagram for ∈ [20,50].…”

Section: Fixmentioning

confidence: 99%

A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

Mahmoud

Abood

2017

Complexity

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Another chaotic nonlinear Lü model with complex factors is covered here. We can build this riotous complex system when we add a complex nonlinear term to the third condition of the complex Lü system and think of it as if every one of the factors is mind boggling or complex. This system in real adaptation is a 6-dimensional continuous autonomous chaotic system. Different types of chaotic complex Lü system are developed. Also, another sort of synchronization is presented by us which is simple for anybody to ponder for the chaotic complex nonlinear system. This sort might be called a complex antilag synchronization (CALS). There are irregular properties for CALS and they do not exist in the literature; for example, (i) the CALS contains or fused two sorts of synchronizations (antilag synchronization ALS and lag synchronization LS); (ii) in CALS the attractors of the main and slave systems are moving opposite or similar to each other with time lag; (iii) the state variable of the main system synchronizes with a different state variable of the slave system. A scheme is intended to accomplish CALS of chaotic complex systems in light of Lyapunov function. The acquired outcomes and effectiveness can be represented by a simulation case for our new model.

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“…The problem of the unidirectional synchronization of chaotic systems consists of finding an appropriate control law such that when this is applied to a system with coupled inputs called "slave" or "response," such system follows the dynamics of an autonomous chaotic system called "master" or "drive" [1][2][3][4][5][6][7][8][9][10][11]. This proper control action is necessary because, without it, two identical autonomous chaotic systems could never be synchronized due to their high sensitivity to initial conditions [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

et al. 2019

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In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.

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Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms

Cited by 25 publications

References 24 publications

A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Application

A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Application

A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

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