Analysis and modified function projective synchronization of integer and fractional-order autonomous Morse jerk oscillator

Yıl 2021, Cilt: 5 Sayı: 2, 275 - 280, 15.08.2021

Dongmo Eric Donald Cyrille Ainamon Alex Stéphane Kemnang Tsafack Nasr Saeed Victor Kamdoum Sifeu T. Kingni

https://doi.org/10.35860/iarej.854623

Öz

Dynamical analysis and modified function projective synchronization (MFPS) of integer and fractional-order Morse jerk oscillator are investigated in this paper. Integer-order Morse jerk oscillator generates periodic behaviors, periodic spiking and two different shapes of chaotic attractors. The periodic spiking and chaotic behaviors obtained during numerical simulations of integer-order Morse jerk oscillator is ascertained by using electronic implementation. The numerical simulations results qualitatively agree with the Orcad-PSpice results. Moreover, MFPS of identical and mismatched chaotic Morse jerk oscillators is numerically investigated. At last, the theoretical investigation of fractional-order Morse jerk oscillator reveals the existence of chaos in Morse jerk oscillator for order greater or equal to 2.85.

Anahtar Kelimeler

Chaos, Electronic implementation, Integer and fractional-order, Modified function projective, Morse jerk oscillator, Periodic spiking oscillations, Synchronization

Kaynakça

• 1. Ivancevic V.G. and T.T. Ivancevic, Complex nonlinearity: chaos, phase transitions, topology change, and path integrals. 2008, Berlin: Springer Science & Business Media.
• 2. Rial J.A., Abrupt climate change: chaos and order at orbital and millennial scales. Global and planetary change, 2004. 41: p. 95-109.
• 3. Carlen E., R. Chatelin, P. Degond and B. Wennberg, Kinetic hirerachy and propagation of chaos in biological swarm models. Physica D: Nonlinear Phenomena, 2013. 260: p. 90-111.
• 4. Callan K. L., L. Illing, Z. Gao, D. J. Gauthier and E. Schöll, Broadband chaos generated by an optoelectronic oscillator. Physical Review Letters, 2010. 104: 113901.
• 5. Kingni S. T., G. Van der Sande, I. V. Ermakov and J. Danckaert, Theoretical analysis of semiconductor ring laser with short and long time-delayed optoelectronic and incoherent feedback. Optics Communications, 2015. 341: p. 147-154.
• 6. Nana B., P. Woafo and S. Domngang, Chaotic synchronization with experimental application to secure communications. Communications in nonlinear science and Numerical Simulation, 2009. 14: p. 2266-2276.
• 7. Kingni S. T., J. H. TallaMbé and P. Woafo, Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography. Chaos, 2012. 22: p. 033108-033115.
• 8. Sprott J. C., Elegant Chaos Algebraically Simple Flows. 2010, Singapore: World Scientific.
• 9. Lindberg E., K. Murali and A. Tamasevicius, The smallest transistor-based nonautonomous chaotic circuit. IEEE Transactions on Circuits and Systems II: Express Briefs, 2005. 52: p. 661-664.
• 10. Tchitnga R., H. B. Fotsin, B. Nana, P. H. L. Fotso and P. Woafo, Hartley’s oscillator: the simplest chaotic two-component circuit. Chaos Solitons Fractals, 2012. 45: p. 306-313.
• 11. Muthuswamy B. and L. O. Chua, Simplest chaotic circuit. International Journal of Bifurcation and Chaos, 2010. 20: p. 1567-1580.
• 12. Piper J. R. and J. C. Sprott, Simple autonomous chaotic circuits, IEEE Transactions on Circuits and Systems II: Express Briefs, 2010. 57: p. 730-734.
• 13. Srisuchinwong B. and B. Munmuangsaen, Current-tunable chaotic jerk oscillator. Electronics letters, 2012. 48: p. 1051-1053.
• 14. Sprott J.C., Simple chaotic systems and circuits. American Journal of Physics, 2000. 68: p. 758-763.
• 15. Acho L., J. Rolon and S. Benitez, Synchronization of mechanical systems with a new Van der Pol chaotic oscillator. WSEAS Transactions on Circuits and Systems, 2004. 3: p. 198-199.
• 16. Benitez S., L. Acho and R. J. R. Guerra, Chaotification of the Van der Pol system using Jerk architecture. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2006. 89: p. 1088-1091.
• 17. Kengne J., Z. T. Njitacke and H. B. Fotsin, Dynamical analysis of a simple autonomous jerk system with multiple attractors, Nonlinear Dynamics, 2016. 83(1): p. 751–765.
• 18. Tavazoei M. S., M. Haeri, A necessary condition for double scroll attractor existence in fractional-order systems. Physics Letters A, 2007. 367(1-2): p.102–13.
• 19. Caponetto R., R. Dongola, L. Fortuna and I. Petraš, Fractional-order system: Modelling and control applications. 2010, World scientific series on nonlinear science, series A, vol. 72.
• 20. Diethelm K., N. J. Ford, D. Freed, A predictor–corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 2002. 29(1): p. 3–22.
• 21. Wu J. and J. Cao, Linear and nonlinear response functions of the Morse oscillator: Classical divergence and the uncertainty principle, The Journal of Chemical Physics, 2001. 115(12): p. 5381-5392.
• 22. Jing Z., J. Deng and J. Yang, Bifurcations of periodic orbits and chaos in damped and driven Morse oscillator. Chaos, Solitons & Fractals, 2008. 35(3): p. 486-505.
• 23. Sudheer K.S. and M. Sabir, Modified function projective synchronization of hyperchaotic systems through open-plus-closed-loop coupling. Physics Letters A, 2010. 374(19-20): p. 2017–2023.
• 24. Kamdoum Tamba V., H. B. Fotsin, J. Kengne, F Kapche Tagne and P. K. Talla, Coupled inductors-based chaotic Colpitts oscillators: Mathematical modeling and synchronization issues. The European Physical Journal Plus, 2015. 130(7):137.