Relevant bibliographies by topics / Rössler Prototype-4 System

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Academic literature on the topic 'Rössler Prototype-4 System'

Author: Grafiati
Published: 4 June 2025
Last updated: 23 June 2025

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Journal articles on the topic "Rössler Prototype-4 System"

1

Sundarapandian, Vaidyanathan. "ADAPTIVE CONTROL AND SYNCHRONIZATION OF RÖSSLER PROTOTYPE-4 SYSTEM." International Journal of Advanced Information Technology (IJAIT) 1, no. 5 (2011): 11–21. https://doi.org/10.5281/zenodo.3374473.

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This paper investigates the adaptive control and synchronization of Rössler prototype-4 system with unknown parameters. The Rössler prototype-4 system is a classical three-dimensional chaotic system studied by O.E. Rössler (1979). First, adaptive control laws are designed to stabilize the Rössler prototype-4 system to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical Rössler prototype-4 systems with unknown parameters. Numerical simulations are shown to validate and illustrate the effectiveness of the proposed adaptive control and synchronization schemes for the Rössler prototype-4 system.
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2

Nikolov, Svetoslav G., and Vassil M. Vassilev. "Dynamics of Rössler Prototype-4 System: Analytical and Numerical Investigation." Mathematics 9, no. 4 (2021): 352. http://dx.doi.org/10.3390/math9040352.

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In this paper, the dynamics of a 3D autonomous dissipative nonlinear system of ODEs-Rössler prototype-4 system, was investigated. Using Lyapunov-Andronov theory, we obtain a new analytical formula for the first Lyapunov’s (focal) value at the boundary of stability of the corresponding equilibrium state. On the other hand, the global analysis reveals that the system may exhibit the phenomena of Shilnikov chaos. Further, it is shown via analytical calculations that the considered system can be presented in the form of a linear oscillator with one nonlinear automatic regulator. Finally, it is found that for some new combinations of parameters, the system demonstrates chaotic behavior and transition from chaos to regular behavior is realized through inverse period-doubling bifurcations.
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3

García, Isaac A., Jaume Llibre, and Susanna Maza. "Periodic orbits and their stability in the Rössler prototype-4 system." Physics Letters A 376, no. 33 (2012): 2234–37. http://dx.doi.org/10.1016/j.physleta.2012.05.035.

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4

Kuate, Paul Didier Kamdem, Achille Ecladore Tchahou Tchendjeu, and Hilaire Fotsin. "A modified Rössler prototype-4 system based on Chua’s diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation." Chaos, Solitons & Fractals 140 (November 2020): 110213. http://dx.doi.org/10.1016/j.chaos.2020.110213.

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5

Vaidyanathan, Sundarapandian V. "Adaptive Control and Synchronization of Rössler Prototype-4 System." SSRN Electronic Journal, 2019. http://dx.doi.org/10.2139/ssrn.3441103.

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6

Kamal, F. M., A. Elsaid, and A. Elsonbaty. "Ghost attractor in fractional order blinking system and its application." Nonlinear Dynamics, April 8, 2022. http://dx.doi.org/10.1007/s11071-022-07391-w.

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AbstractIn this paper, the occurrence of ghost attractor is verified in three cases of a proposed fractional order Rössler blinking system. Firstly, the dynamical behaviors of the short memory fractional order prototype-4 Rössler system with Chua’s diode are explored via bifurcation diagrams and Lyapunov exponents. It is depicted that this system exhibits a variety of dynamics including limit cycles, period doubling and chaos. Then, a proposed non-autonomous fractional order Rössler blinking system is introduced. Numerical simulations are employed to confirm the existence of ghost attractors at specific cases which involve very fast switching time between two composing autonomous fractional subsystems. It is found that the presented fractional order blinking system is very sensitive to system parameters, initial conditions, and stochastic process parameters. Thus, the induced chaotic ghost attractor is utilized in a suggested ghost attractor-based chaotic image encryption scheme for first time. Finally, a detailed security analysis is carried out and reveals that the proposed image cryptosystem is immune against different types of attacks such as differential attacks, brute force attacks, cropping and statistical attacks.
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Book chapters on the topic "Rössler Prototype-4 System"

1

"Rössler Prototype-4 System." In Elegant Automation. WORLD SCIENTIFIC, 2023. http://dx.doi.org/10.1142/9789811277528_0024.

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