Synchronization and Stabilization of Chaotic Dynamics in a Quasi-1D Bose-Einstein Condensate

Idowu, Babatunde A.; Vincent, U. E.

doi:10.1155/2013/723581

Cited by 13 publications

(9 citation statements)

References 43 publications

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“…e synchronization phenomena among dynamical systems are a widely studied topic in the last decades due to the vast amount of applications in science and engineering [1][2][3]. In the related literature, dynamical systems and synchronization applications in many fields can be found, from biology [4,5], mechanical systems [6][7][8][9], chemistry [10], physics [11,12], fuzzy modeling [13][14][15][16] to secure communications [17][18][19], among many others. In general, it is said that a set of dynamical systems achieve synchronization if trajectories in each system approach a common trajectory.…”

Section: Introductionmentioning

confidence: 99%

Mamdani‐Type Fuzzy‐Based Adaptive Nonhomogeneous Synchronization

2021

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The aim of this work is the design of an adaptive controller based on Mamdani-type fuzzy inference systems. The input control is constructed with saturation functions’ fuzzy-equivalents, which works as the adaptive scheme of the controller. This control law is designed to stabilize the error system to synchronize a pair of chaotic nonhomogeneous piecewise systems. Finally, an illustrative example as numerical evidence is developed.

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Section: Introductionmentioning

confidence: 99%

Mamdani‐Type Fuzzy‐Based Adaptive Nonhomogeneous Synchronization

2021

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“…This myth vanished in 1983 thanks to Yamada and Fujisaka [6] where a methodology for the synchronization of two chaotic systems using bidirectional coupling is presented, meanwhile in 1990 Pecora and Carroll [7] proposed the synchronization of the drive and response systems with different initial conditions. Since then, a wide series of alternative methodologies for the synchronization of chaotic systems have been developed [8][9][10][11][12][13][14][15][16] and thanks to this methodologies, a vast quantity of possible applications have been found in science and engineering, from physics [17,18], optics [19,20], biology [21][22][23], chemistry [24,25] and specially in the branch of secure communications [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

Pulido-Luna

López-Rentería

Cázarez-Castro

2020

MCA

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In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes.

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“…The adaptive fuzzy systems are used for estimating some unknown nonlinear functions, see [43]. In achieving synchroniza tion many methods have been proposed such as active control [44,45,46,47,48], backstepping [49,50], adaptive backstepping [51,52,53,54], sliding mode, and so on.…”

Section: Introductionmentioning

confidence: 99%

Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

Idowu

Oyeleke

Ogabi

et al. 2020

JRRS

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Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

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Synchronization and Stabilization of Chaotic Dynamics in a Quasi-1D Bose-Einstein Condensate

Cited by 13 publications

References 43 publications

Mamdani‐Type Fuzzy‐Based Adaptive Nonhomogeneous Synchronization

Mamdani‐Type Fuzzy‐Based Adaptive Nonhomogeneous Synchronization

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

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