On the Rossler Attractor

Year 2020, Volume: 2 Issue: 1, 1 - 2, 30.06.2020

Otto E. Rossler

Abstract

I feel chaos theory still is one of the greatest fields. The study of chaos represents the most complicated steady-state behavior known in dynamical systems. Recent years have seen rapid improvements in integer and fractional-order chaotic systems with engineering applications. Chaos-based applications form an important issue in both science and engineering. Novel chaotic systems have been presented in recent engineering applications. Many studies have been done on the basis of well-known systems with chaotic attractors, including also the Lorenz, the Chua, and the Chen system.

Keywords

Chaos, Rossler Attractor

Thanks

I thank Dr. Akif Akgül for stimulation.

References

• Abundiz-Pérez, F., C. Cruz-Hernández, M. Murillo-Escobar, R. López-Gutiérrez, and A. Arellano-Delgado, 2016 A fingerprint image encryption scheme based on hyperchaotic rössler map. Mathe-matical Problems in Engineering 2016.
• Barrio, R., F. Blesa, and S. Serrano, 2009 Qualitative analysis of the rössler equations: Bifurcations of limit cycles and chaotic attractors. Physica D: Nonlinear Phenomena 238: 1087–1100.
• Cafagna, D. and G. Grassi, 2009 Hyperchaos in the fractional-order rössler system with lowest-order. International Journal of Bifurcation and Chaos 19: 339–347.
• Girdhar, A. and V. Kumar, 2018 A rgb image encryption technique using lorenz and rossler chaotic system on dna sequences. Multimedia Tools and Applications 77: 27017–27039.
• He, W.-P., L. Wang, Y.-D. Jiang, and S.-Q. Wan, 2016 An improved method for nonlinear parameter estimation: a case study of the rössler model. Theoretical and applied climatology 125: 521–528.
• Hsieh, J.-Y., C.-C. Hwang, A.-P. Wang, and W.-J. Li, 1999 Controlling hyperchaos of the rossler system. International Journal of Control 72: 882–886.
• Koyuncu, I., I. Sahin, C. Gloster, and N. K. Sarıtekin, 2017 A neuron library for rapid realization of artificial neural networks on fpga: A case study of rössler chaotic system. Journal of Circuits, Systems and Computers 26: 1750015.
• Minati, L., H. Ito, A. Perinelli, L. Ricci, L. Faes, et al., 2019 Connectivity influences on nonlinear dynamics in weakly-synchronized networks: Insights from rössler systems, electronic chaotic oscillators, model and biological neurons. IEEE Access 7: 174793–174821.
• Nikolov, S. and S. Clodong, 2006 Hyperchaos–chaos–hyperchaos transition in modified rössler systems. Chaos, solitons & fractals 28: 252–263.
• Razminia, A., V. J. Majd, and D. Baleanu, 2011 Chaotic incommensurate fractional order rössler system: active control and synchronization. Advances in Dif-ference Equations 2011: 15.
• Rössler, O. E., 1976 An equation for continuous chaos. Physics Letters A 57: 397–398.
• Schmitz, J. and L. Zhang, 2017 Rössler-based chaotic communication system implemented on fpga. In 2017 IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE), pp. 1–4, IEEE.
• Sunny, J., J. Schmitz, and L. Zhang, 2018 Artificial neural network modelling of rossler’s and chua’s chaotic systems. In 2018 IEEE Canadian Conference on Electri-cal & Computer Engineering (CCECE), pp. 1–4, IEEE.
• Taskiran, Z. G. C. and H. Sedef, 2020 Realization of memristor-based chaotic rossler circuit. Journal of the Faculty of Engineering and Architecture of Gazi University 35: 765–774.