Dynamical Analysis, Electronic Circuit Design and Control Application of a Different Chaotic System

Year 2020, Volume: 2 Issue: 1, 10 - 16, 30.06.2020

Yusuf Adıyaman Selcuk Emiroglu Muhammed Kürşad Uçar Muhammed Yıldız

Abstract

In this study, the dynamic behavior of a chaotic system is explored and its dynamical analysis is performed by Lyapunov exponents, fractional dimension, dependence to initial conditions and bifurcation diagram. In addition, the bifurcation analysis of the system is studied with respect to a certain parameter. The electronic circuit implementation of a chaotic system is realized and compared with the phase portraits obtained from Matlab and circuit realization. Also, passive control technique is applied to stabilize and suppress the chaos in the chaotic system. Numerical simulations are presented to verify the theoretical analysis and the effectiveness of the proposed control method.

Keywords

Computer, Electronic

References

• Akgul, A., H. Calgan, I. Koyuncu, I. Pehlivan, and A. Istanbullu, 2016a Chaos-based engineering applications with a 3d chaotic system without equilibrium points. Nonlinear dynamics 84: 481– 495.
• Akgul, A., S. Kacar, and B. Aricioglu, 2017 A new two-level data hiding algorithm for high security based on a nonlinear system. Nonlinear Dynamics 90: 1123–1140.
• Akgul, A., I. Moroz, I. Pehlivan, and S. Vaidyanathan, 2016b A new four-scroll chaotic attractor and its engineering applications. Optik 127: 5491–5499.
• Asadollahi, M., A. R. Ghiasi, and M. A. Badamchizadeh, 2020 Adaptive control for a class of nonlinear chaotic systems with quantized input delays. Journal of the Franklin Institute .
• Azarang, A., S. Kamaei, M. Miri, and M. H. Asemani, 2016 A new fractional-order chaotic system and its synchronization via lyapunov and improved laplacian-based method. Optik 127: 11717–11731.
• Çavusoglu, Ü., A. Akgül, A. Zengin, and I. Pehlivan, 2017 The design and implementation of hybrid rsa algorithm using a novel chaos based rng. Chaos, Solitons & Fractals 104: 655–667.
• Emiroglu, S. and Y. Uyaroglu, 2010 Control of Rabinovich chaotic system based on passive control. Scientific Research and Essays 5: 3298–3305.
• Fu, S., Y. Liu, H. Ma, and Y. Du, 2020 Control chaos to different stable states for a piecewise linear circuit system by a simple linear control. Chaos, Solitons and Fractals 130: 109431.
• Kai, G., W. Zhang, Z. Wei, J. Wang, and A. Akgul, 2017 Hopf bifurcation, positively invariant set, and physical realization of a new four-dimensional hyperchaotic financial system. Mathematical Problems in Engineering 2017.
• Kocamaz, U. E., Y. Uyaro˘ glu, and H. Kızmaz, 2017 Controlling hyperchaotic Rabinovich system with single state controllers: Comparison of linear feedback, sliding mode, and passive control methods. Optik 130: 914–921.
• Koyuncu, I., M. Tuna, I. Pehlivan, C. B. Fidan, and M. Alçın, 2020 Design, fpga implementation and statistical analysis of chaosring based dual entropy core true random number generator. Analog Integrated Circuits and Signal Processing 102: 445–456.
• Lai, Q., A. Akgul, C. Li, G. Xu, and Ü. Çavu¸so˘ glu, 2018 A new chaotic system with multiple attractors: Dynamic analysis, circuit realization and s-box design. Entropy 20: 12.
• Li, C., A. Akgul, J. C. Sprott, H. H. Iu, and W. J.-C. Thio, 2018 A symmetric pair of hyperchaotic attractors. International Journal of Circuit Theory and Applications 46: 2434–2443.
• Lorenz, E. N., 1963 Deterministic nonperiodic flow. Journal of the atmospheric sciences 20: 130–141.
• Ott, E., C. Grebogi, and J. A. Yorke, 1990 Controlling chaos. Physical Review Letters 64: 1196–1199.
• Pham, V.-T., A. Akgul, C. Volos, S. Jafari, and T. Kapitaniak, 2017 Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variable. AEU-International Journal of Electronics and Communications 78: 134–140.
• Qi, D., G. Zhao, and Y. Song, 2004 Passive control of Chen chaotic system. In Proceedings of the World Congress on Intelligent Control and Automation (WCICA), volume 2, pp. 1284–1286.
• Rajagopal, K., M. Tuna, A. Karthikeyan, ˙I. Koyuncu, P. Duraisamy, et al., 2019 Dynamical analysis, sliding mode synchronization of a fractional-order memristor hopfield neural network with parameter uncertainties and its non-fractional-order fpga implementation. The European Physical Journal Special Topics 228: 2065–2080.
• Ren, S., S. Panahi, K. Rajagopal, A. Akgul, V.-T. Pham, et al., 2018 A new chaotic flow with hidden attractor: The first hyperjerk system with no equilibrium. Zeitschrift für Naturforschung A 73: 239–249.
• Tuna, M. and C. B. Fidan, 2016 Electronic circuit design, implementation and fpga-based realization of a new 3d chaotic system with single equilibrium point. Optik 127: 11786–11799.
• Tuna, M., A. Karthikeyan, K. Rajagopal, M. Alcin, and ˙I. Koyuncu, 2019 Hyperjerk multiscroll oscillators with megastability: Analysis, fpga implementation and a novel ann-ring-based true random number generator. AEU-International Journal of Electronics and Communications 112: 152941.
• Uyaroglu, Y. and S. Emiroglu, 2015 Passivity-based chaos control and synchronization of the four dimensional Lorenz-Stenflo system via one input. JVC/Journal of Vibration and Control 21: 1657–1664.
• Uyaroˇ glu, Y., M. Varan, and S. Emiroˇ glu, 2012 Chaotic ferroresonance and its control with sliding mode technique for voltage transformer circuits: A case study of manual single phase switching operation in three-phase transmission system. Optoelectronics and Advanced Materials, Rapid Communications 6.
• Vaidyanathan, S., I. Pehlivan, L. G. Dolvis, K. Jacques, M. Alcin, et al., 2020 A novel ann-based four-dimensional two-disk hyperchaotic dynamical system, bifurcation analysis, circuit realisation and fpga-based trng implementation. International Journal of Computer Applications in Technology 62: 20–35.
• Varan, M. and A. Akgul, 2018 Control and synchronisation of a novel seven-dimensional hyperchaotic system with active control. Pramana 90: 54.
• Wang, Z., A. Akgul, V.-T. Pham, and S. Jafari, 2017 Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors. Nonlinear Dynamics 89: 1877–1887.
• Wei, Z., A. Akgul, U. E. Kocamaz, I. Moroz, and W. Zhang, 2018 Control, electronic circuit application and fractional-order analysis of hidden chaotic attractors in the self-exciting homopolar disc dynamo. Chaos, Solitons & Fractals 111: 157–168.
• Yu,W., 1999 Passive equivalence of chaos in Lorenz system. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 46: 876–878.