Araştırma Makalesi
Yıl 2023,
Cilt: 11 Sayı: 3, 184 - 190, 30.09.2023
Öz
In this study, the incommensurate fractional-order King Cobra (IFKC) chaotic system has been investigated. Through bifurcation diagrams and Lyapunov exponent spectra, it has been determined that the IFKC system exhibits rich dynamics. Subsequently, using the Proportional Tilt Integral Derivative (P-TID) control method, synchronization of two IFKC chaotic systems with different initial values has been achieved. Upon examination of the obtained simulation results, it has been demonstrated that the identified IFKC chaotic system and the P-TID controller can be effectively utilized for secure communication.
Anahtar Kelimeler
Incommensurate fractional-order chaos synchronization TID control
Kaynakça
- M. Demirtas, E. Ilten, and H. Calgan, “Pareto-based multi-objective optimization for fractional order PIλ speed control of induction motor by using Elman Neural Network,” Arab. J. Sci. Eng., vol. 44, no. 3, pp. 2165–2175, 2019.
- Z. Wei, A. Akgul, U. E. Kocamaz, I. Moroz, and W. Zhang, “Control, electronic circuit application and fractional-order analysis of hidden chaotic attractors in the self-exciting homopolar disc dynamo,” Chaos, Solitons & Fractals, vol. 111, pp. 157–168, 2018.
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- M. Odabaşı, “Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations,” An Int. J. Optim. Control Theor. Appl., vol. 11, no. 1, pp. 52–58, 2021.
- A. A. Hamou, R. R. Q. Rasul, Z. Hammouch, and N. Özdemir, “Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco,” Comput. Appl. Math., vol. 41, no. 6, p. 289, 2022.
- D. Avcı and F. Soytürk, “Optimal control strategies for a computer network under virus threat,” J. Comput. Appl. Math., vol. 419, p. 114740, 2023.
- I. Grigorenko and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Phys. Rev. Lett., vol. 91, no. 3, p. 34101, 2003.
- T. T. Hartley, C. F. Lorenzo, and H. K. Qammer, “Chaos in a fractional order Chua’s system,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 42, no. 8, pp. 485–490, 1995.
- A. Gokyildirim, H. Calgan, and M. Demirtas, “Fractional-Order sliding mode control of a 4D memristive chaotic system,” J. Vib. Control, p. 10775463231166188, 2023.
- A. Akgul, C. Arslan, and B. Arıcıoglu, “Design of an interface for random number generators based on integer and fractional order chaotic systems,” Chaos Theory Appl., vol. 1, no. 1, pp. 1–18, 2019.
- A. Akgul, Y. Adiyaman, A. Gokyildirim, B. Aricioglu, M. A. Pala, and M. E. Cimen, “Electronic circuit implementations of a fractional-order chaotic system and observing the escape from chaos,” J. Circuits, Syst. Comput., vol. 32, no. 05, p. 2350085, Mar. 2023.
- O. Atan, M. Turk, and R. Tuntas, “Fractional order controller design for fractional order chaotic synchronization.,” Int. J. Nat. Eng. Sci., vol. 7, no. 3, 2013.
- G. Xu, S. Zhao, and Y. Cheng, “Chaotic synchronization based on improved global nonlinear integral sliding mode control☆,” Comput. Electr. Eng., vol. 96, p. 107497, 2021.
- F. Motallebzadeh, M. R. J. Motlagh, and Z. R. Cherati, “Synchronization of different-order chaotic systems: Adaptive active vs. optimal control,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 9, pp. 3643–3657, 2012.
- C. Ge, C. Hua, and X. Guan, “Master-slave synchronization criteria of Lur’e systems with time-delay feedback control,” Appl. Math. Comput., vol. 244, pp. 895–902, 2014.
- S. Çiçek, A. Ferikoglu, and I. Pehlivan, “A new 3D chaotic system: Dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application,” Optik (Stuttg)., vol. 127, no. 8, pp. 4024–4030, 2016.
- S. Keyong, B. Ruixuan, G. Wang, W. Qiutong, and Z. Yi, “Passive synchronization control for integer-order chaotic systems and fractional-order chaotic systems,” in 2019 Chinese Control Conference (CCC), 2019, pp. 1115–1119.
- Z.-A. S. A. Rahman, H. A. A. Al-Kashoash, S. M. Ramadhan, and Y. I. A. Al-Yasir, “Adaptive control synchronization of a novel memristive chaotic system for secure communication applications,” Inventions, vol. 4, no. 2, p. 30, 2019.
- P. Alexander, S. Emiroğlu, S. Kanagaraj, A. Akgul, and K. Rajagopal, “Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization,” Eur. Phys. J. B, vol. 96, no. 1, p. 12, 2023.
- A. Gokyildirim, U. E. Kocamaz, Y. Uyaroglu, and H. Calgan, “A novel five-term 3D chaotic system with cubic nonlinearity and its microcontroller-based secure communication implementation,” AEU - Int. J. Electron. Commun., vol. 160, p. 154497, Feb. 2023.
- C. Ma, J. Mou, J. Liu, F. Yang, H. Yan, and X. Zhao, “Coexistence of multiple attractors for an incommensurate fractional-order chaotic system,” Eur. Phys. J. Plus, vol. 135, pp. 1–21, 2020.
- P. Muthukumar, P. Balasubramaniam, and K. Ratnavelu, “Synchronization and an application of a novel fractional order King Cobra chaotic system,” Chaos An Interdiscip. J. Nonlinear Sci., vol. 24, no. 3, 2014.
- A. Gokyildirim, “Circuit realization of the fractional-order Sprott K chaotic system with standard components,” Fractal Fract., vol. 7, no. 6, p. 470, 2023.
- K. Rajagopal et al., “Multistability and coexisting attractors in a new circulant chaotic system,” Int. J. Bifurc. Chaos, vol. 29, no. 13, p. 1950174, 2019.
- M. S. Tavazoei and M. Haeri, “A necessary condition for double scroll attractor existence in fractional-order systems,” Phys. Lett. A, vol. 367, no. 1–2, pp. 102–113, 2007.
- M.-F. Danca, “Matlab code for Lyapunov exponents of fractional-order systems, part ii: The noncommensurate case,” Int. J. Bifurc. Chaos, vol. 31, no. 12, p. 2150187, 2021.
- A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Phys. D Nonlinear Phenom., vol. 16, no. 3, pp. 285–317, Jul. 1985.
- S. Emiroglu, A. Akgül, Y. Adıyaman, T. E. Gümüş, Y. Uyaroglu, and M. A. Yalçın, “A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization,” Circuit World, vol. 48, no. 2, pp. 265–277, 2022.
- H. Calgan and M. Demirtas, “Design and implementation of fault tolerant fractional order controllers for the output power of self-excited induction generator,” Electr. Eng., vol. 103, no. 5, pp. 2373–2389, 2021.
- T. Amieur, M. Bechouat, M. Sedraoui, S. Kahla, and H. Guessoum, “A new robust tilt-PID controller based upon an automatic selection of adjustable fractional weights for permanent magnet synchronous motor drive control,” Electr. Eng., pp. 1–18, 2021.
- S. Matlab, “Matlab,” MathWorks, Natick, MA, 2012.
- H. Li, Y. Shen, Y. Han, J. Dong, and J. Li, “Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle,” Chaos, Solitons & Fractals, vol. 168, p. 113167, 2023.
Yıl 2023,
Cilt: 11 Sayı: 3, 184 - 190, 30.09.2023
Öz
Kaynakça
- M. Demirtas, E. Ilten, and H. Calgan, “Pareto-based multi-objective optimization for fractional order PIλ speed control of induction motor by using Elman Neural Network,” Arab. J. Sci. Eng., vol. 44, no. 3, pp. 2165–2175, 2019.
- Z. Wei, A. Akgul, U. E. Kocamaz, I. Moroz, and W. Zhang, “Control, electronic circuit application and fractional-order analysis of hidden chaotic attractors in the self-exciting homopolar disc dynamo,” Chaos, Solitons & Fractals, vol. 111, pp. 157–168, 2018.
- E. Ilten and M. Demirtas, “Fractional order super-twisting sliding mode observer for sensorless control of induction motor,” COMPEL - Int. J. Comput. Math. Electr. Electron. Eng., vol. 38, no. 2, pp. 878–892, Mar. 2019.
- M. Odabaşı, “Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations,” An Int. J. Optim. Control Theor. Appl., vol. 11, no. 1, pp. 52–58, 2021.
- A. A. Hamou, R. R. Q. Rasul, Z. Hammouch, and N. Özdemir, “Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco,” Comput. Appl. Math., vol. 41, no. 6, p. 289, 2022.
- D. Avcı and F. Soytürk, “Optimal control strategies for a computer network under virus threat,” J. Comput. Appl. Math., vol. 419, p. 114740, 2023.
- I. Grigorenko and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Phys. Rev. Lett., vol. 91, no. 3, p. 34101, 2003.
- T. T. Hartley, C. F. Lorenzo, and H. K. Qammer, “Chaos in a fractional order Chua’s system,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 42, no. 8, pp. 485–490, 1995.
- A. Gokyildirim, H. Calgan, and M. Demirtas, “Fractional-Order sliding mode control of a 4D memristive chaotic system,” J. Vib. Control, p. 10775463231166188, 2023.
- A. Akgul, C. Arslan, and B. Arıcıoglu, “Design of an interface for random number generators based on integer and fractional order chaotic systems,” Chaos Theory Appl., vol. 1, no. 1, pp. 1–18, 2019.
- A. Akgul, Y. Adiyaman, A. Gokyildirim, B. Aricioglu, M. A. Pala, and M. E. Cimen, “Electronic circuit implementations of a fractional-order chaotic system and observing the escape from chaos,” J. Circuits, Syst. Comput., vol. 32, no. 05, p. 2350085, Mar. 2023.
- O. Atan, M. Turk, and R. Tuntas, “Fractional order controller design for fractional order chaotic synchronization.,” Int. J. Nat. Eng. Sci., vol. 7, no. 3, 2013.
- G. Xu, S. Zhao, and Y. Cheng, “Chaotic synchronization based on improved global nonlinear integral sliding mode control☆,” Comput. Electr. Eng., vol. 96, p. 107497, 2021.
- F. Motallebzadeh, M. R. J. Motlagh, and Z. R. Cherati, “Synchronization of different-order chaotic systems: Adaptive active vs. optimal control,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 9, pp. 3643–3657, 2012.
- C. Ge, C. Hua, and X. Guan, “Master-slave synchronization criteria of Lur’e systems with time-delay feedback control,” Appl. Math. Comput., vol. 244, pp. 895–902, 2014.
- S. Çiçek, A. Ferikoglu, and I. Pehlivan, “A new 3D chaotic system: Dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application,” Optik (Stuttg)., vol. 127, no. 8, pp. 4024–4030, 2016.
- S. Keyong, B. Ruixuan, G. Wang, W. Qiutong, and Z. Yi, “Passive synchronization control for integer-order chaotic systems and fractional-order chaotic systems,” in 2019 Chinese Control Conference (CCC), 2019, pp. 1115–1119.
- Z.-A. S. A. Rahman, H. A. A. Al-Kashoash, S. M. Ramadhan, and Y. I. A. Al-Yasir, “Adaptive control synchronization of a novel memristive chaotic system for secure communication applications,” Inventions, vol. 4, no. 2, p. 30, 2019.
- P. Alexander, S. Emiroğlu, S. Kanagaraj, A. Akgul, and K. Rajagopal, “Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization,” Eur. Phys. J. B, vol. 96, no. 1, p. 12, 2023.
- A. Gokyildirim, U. E. Kocamaz, Y. Uyaroglu, and H. Calgan, “A novel five-term 3D chaotic system with cubic nonlinearity and its microcontroller-based secure communication implementation,” AEU - Int. J. Electron. Commun., vol. 160, p. 154497, Feb. 2023.
- C. Ma, J. Mou, J. Liu, F. Yang, H. Yan, and X. Zhao, “Coexistence of multiple attractors for an incommensurate fractional-order chaotic system,” Eur. Phys. J. Plus, vol. 135, pp. 1–21, 2020.
- P. Muthukumar, P. Balasubramaniam, and K. Ratnavelu, “Synchronization and an application of a novel fractional order King Cobra chaotic system,” Chaos An Interdiscip. J. Nonlinear Sci., vol. 24, no. 3, 2014.
- A. Gokyildirim, “Circuit realization of the fractional-order Sprott K chaotic system with standard components,” Fractal Fract., vol. 7, no. 6, p. 470, 2023.
- K. Rajagopal et al., “Multistability and coexisting attractors in a new circulant chaotic system,” Int. J. Bifurc. Chaos, vol. 29, no. 13, p. 1950174, 2019.
- M. S. Tavazoei and M. Haeri, “A necessary condition for double scroll attractor existence in fractional-order systems,” Phys. Lett. A, vol. 367, no. 1–2, pp. 102–113, 2007.
- M.-F. Danca, “Matlab code for Lyapunov exponents of fractional-order systems, part ii: The noncommensurate case,” Int. J. Bifurc. Chaos, vol. 31, no. 12, p. 2150187, 2021.
- A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Phys. D Nonlinear Phenom., vol. 16, no. 3, pp. 285–317, Jul. 1985.
- S. Emiroglu, A. Akgül, Y. Adıyaman, T. E. Gümüş, Y. Uyaroglu, and M. A. Yalçın, “A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization,” Circuit World, vol. 48, no. 2, pp. 265–277, 2022.
- H. Calgan and M. Demirtas, “Design and implementation of fault tolerant fractional order controllers for the output power of self-excited induction generator,” Electr. Eng., vol. 103, no. 5, pp. 2373–2389, 2021.
- T. Amieur, M. Bechouat, M. Sedraoui, S. Kahla, and H. Guessoum, “A new robust tilt-PID controller based upon an automatic selection of adjustable fractional weights for permanent magnet synchronous motor drive control,” Electr. Eng., pp. 1–18, 2021.
- S. Matlab, “Matlab,” MathWorks, Natick, MA, 2012.
- H. Li, Y. Shen, Y. Han, J. Dong, and J. Li, “Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle,” Chaos, Solitons & Fractals, vol. 168, p. 113167, 2023.
Toplam 32 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Hesaplama Teorisi (Diğer) |
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Erken Görünüm Tarihi | 30 Eylül 2023 |
| Yayımlanma Tarihi | 30 Eylül 2023 |
| Gönderilme Tarihi | 26 Ağustos 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 11 Sayı: 3 |
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