دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,531
تعداد مقالات18,660
تعداد مشاهده مقاله61,385,238
تعداد دریافت فایل اصل مقاله22,142,345
Rasul, Tahsin, Salih, Rizgar. (1405). Hopf bifurcation and chaotic attractors in two special jerk system cases. سامانه مدیریت نشریات علمی, 14(2), 678-689. doi: 10.22034/cmde.2024.61865.2694
Tahsin I Rasul; Rizgar H. Salih. "Hopf bifurcation and chaotic attractors in two special jerk system cases". سامانه مدیریت نشریات علمی, 14, 2, 1405, 678-689. doi: 10.22034/cmde.2024.61865.2694
Rasul, Tahsin, Salih, Rizgar. (1405). 'Hopf bifurcation and chaotic attractors in two special jerk system cases', سامانه مدیریت نشریات علمی, 14(2), pp. 678-689. doi: 10.22034/cmde.2024.61865.2694
Rasul, Tahsin, Salih, Rizgar. Hopf bifurcation and chaotic attractors in two special jerk system cases. سامانه مدیریت نشریات علمی, 1405; 14(2): 678-689. doi: 10.22034/cmde.2024.61865.2694

Hopf bifurcation and chaotic attractors in two special jerk system cases

Computational Methods for Differential Equations
مقاله 12، دوره 14، شماره 2، تیر 2026، صفحه 678-689    اصل مقاله (1.1 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61865.2694
نویسندگان
Tahsin I Rasul* 1؛ Rizgar H. Salih2
1Department of Mathematics, Faculty of Science, Soran University, Soran, Kurdistan Region, Iraq.
2Department of Mathematics, College of Basic Education, University of Raparin, Rania, Kurdistan Region, Iraq.
چکیده
This paper investigates the Hopf bifurcation with self-excited and hidden chaotic attractors in special types of chaotic jerk systems. The stability of the equilibrium points and Hopf bifurcation are rigorously analyzed for the proposed systems. It is remarkable to analyze the Hopf bifurcation using focus quantity techniques. These bifurcations can be either supercritical or subcritical, depending on the control parameters. The dynamic behavior of the systems, an analysis of self-excited chaotic attractors and hidden chaotic attractors was performed. Additionally, bifurcation analysis and evaluation of Lyapunov exponents revealed complex transitions among periodic, self-excited chaotic and hidden chaotic attractors as the system parameters varied. It was found that the systems exhibit both self-excited and hidden attractors, as demonstrated by the bifurcation diagrams, Lyapunov exponents and cross sections. All of the results provided in this study were acquired applying the Maple and Matlab software.
کلیدواژه‌ها
Jerk system؛ Hopf bifurcation؛ Chaotic؛ Self-excited attractors and Hidden attractors
مراجع
  • [1] A. O. Almatroud, A. E. Matouk, et al., Self-Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems, Discrete Dyn. Nat. Soc., 1 (2022), 6458027.
  • [2] A. Ali and S. Jawad, Stability analysis of the depletion of dissolved oxygen for the Phytoplankton-Zooplankton model in an aquatic environment, Iraqi J. Sci., (2024), 2736–2748.
  • [3] A. Ali, S. Jawad, A. H. Ali, and M. Winte, Stability analysis for the phytoplankton-zooplankton model with depletion of dissolved oxygen and strong Allee effects, Results Eng., 22 (2024), 102190.
  • [4] K. Barati, S. Jafari, J. C. Sprott, and V. T. Pham, Simple chaotic flows with a curve of equilibria, IJBC., 26(12) (2016), 1630034.
  • [5] T. Bonny, S. Vaidyanathan, A. Sambas, K. Benkouide, W. A. Nassan, and O. Naqaweh, Multistability and bifurcation analysis of a novel 3d jerk system: Electronic circuit design, fpga implementation, and image cryptography scheme, IEEE Access., 44 (2023).
  • [6] R. Chase Harrison, B. K. Rhea, A. R. Oldag, R. N. Dean, and E. Perkins, Experimental Validation of a Chaotic Jerk Circuit Based True Random Number Generator, Chaos Theory Appl., 4 (2022), 64-70.
  • [7] G. Chen and T. Ueta, Yet another chaotic attractor, IJBC., 9(07) (1999), 1465-1466.
  • [8] Y. Dong, H. Liu, Y. Wei, Q. Zhang, and G. Ma, Stability and Hopf Bifurcation Analysis of a Predator–Prey Model with Weak Allee Effect Delay and Competition Delay, Mathematics (MDPI), 12(18) (2022), 2853.
  • [9] O. De Oliveira, The Implicit and the Inverse Function theorems: easy proofs, Real Anal. Exchange, 39(1) (2013), 207-218.
  • [10] Y. Feng and W. Pan, Hidden attractors without equilibrium and adaptive reducedorder function projective synchronization from hyperchaotic rikitake system, Pramana, 88(4) (2017), 1-6.
  • [11] J. Golmankhaneh and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer Science & Business Media, 42 (2013).
  • [12] G. Gakam Tegue, J. Nkapkop, et al., A novel image encryption scheme based on compressive sensing, elliptic curves and a new jerk oscillator with multistability, Phys. Scr., 59 (2022), 125215.
  • [13] A. M. Husien and A. I. Amen, Hopf and Zero-Hopf Bifurcation Analysis for a Chaotic System, IJBC., 34(08) (2024), 2450104.
  • [14] B. D. Hassard, N. D. Kazarinoff, Y. H. Wan, and Y. W. Wan, Theory and applications of Hopf bifurcation, CUP Archive, 41 (1981).
  • [15] S. Jafari, J. C. Sprott, and M. Molaie, A simple chaotic flow with a plane of equilibria, IJBC., 26 (2016),1650098.
  • [16] S. Jafari, J. C. Sprott, and M. Molaie, Simple chaotic flows with a line equilibrium, Chaos, Solitons & Fractals., 57 (2013), 79-84.
  • [17] S. Jawad, et al., Dynamical behavior of a cancer growth model with chemotherapy and boosting of the immune system, Mathematics, 11(2) (2023), 406.
  • [18] M. Joshi and A. Ranjan, Autonomous simple chaotic jerk system with stable and unstable equilibria using reverse sine hyperbolic functions, IJBC., 30 (2020), 2050070.
  • [19] J. Kengne, Z. T. Njitacke, A. Nguomkam Negou, M. Fouodji Tsostop, and H. B. Fotsin, Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit, IJBC., 26(05) (2016), 1650081.
  • [20] N. V. Kuznetsov, G. A. Leonov, and V. I. Vagaitsev, Analytical-numerical method for attractor localization of generalized chua’s system, IFAC Proceedings Volumes, 43(11) (2010),29-33.
  • [21] S. G. Krantz and H. R. Parks, The implicit function theorem: history, theory, and applications, Springer Science & Business Media, 2012.
  • [22] J. Lu and G. Chen, A new chaotic attractor coined, IJBC., 12(03) (2002), 659-661 .
  • [23] F. Li and J. Zeng, Multi-scroll attractor and multi-stable dynamics of a three dimensional jerk system, Energies., 16(5) (2023), 2494.
  • [24] C. Lăzureanu, Dynamical properties, deformations, and chaos in a class of inversion invariant jerk equations, Symmetry (MDPI), 14(7) (2022),1318.
  • [25] W. M. Liu, Criterion of Hopf bifurcation without using eigenvalues, J. Math. Anal. Appl., 182(1) (1994), 250–256.
  • [26] R. May, Simple mathematical models with very complicated dynamics, Nature, 261 (1976), 459-467 .
  • [27] J. M. Munoz-Pacheco, E. Zambrano-Serrano, et al., A new fractional-order chaotic system with different families of hidden and self-excited attractors, Entropy, 20(08) (2018), 564 .
  • [28] S. Ozbal, H. C. Sudor, and A. U. Keskin, Chaotic dynamics of a jerk function with hyperbolic tangent nonlinearity, IEEE., 20 (2018), 1-4.
  • [29] V. T. Pham, S. Jafari, T. Kapitaniak, C. Volo, and S. T. Kingni, Generating a chaotic system with one stable equilibrium, IJBC., 27(04) (2017),1750053.
  • [30] L. S. Pontryagin, Ordinary Differential Equations, Adiwes International Series in Mathematics., Elsevier, 2014.
  • [31] T. I. Rasul and R. H. Salih, Bifurcation analysis with chaotic attractor for a special case of jerk system, Phy. Scr., 99(8) (2024),085235.
  • [32] K. Rajagopal, S. K. Takougang, et al., Autonomous jerk oscillator with cosine hyperbolic nonlinearity: analysis, fpga implementation, and synchronization, Adv. Math. Phys., (2018).
  • [33] B. Ramakrishnan, C. Welba, A. C Chamgou´e, A. Karthikeyan, and S. T. Kingni, Autonomous jerk oscillator with sine nonlinearity and logistic map for sEMG encryption, Phys. Scr., 97(05) (2022), 095211.
  • [34] O. R¨ossler, An equation for hyperchaos, Physics Letters A., 71(2-3) (1979), 155-15.
  • [35] B. Sang, X. Hu, and N. Wang, The chaotic mechanisms in some jerk systems, Electron. J. Qual. Theory Differ. Equ., 7 (2022), 15714-15740.
  • [36] R. H. Salih and B. M. Mohammed, Stability and Hopf Bifurcation in a Modified Sprott System, Tatra Mt. Math. Pu., (2024), 1-14.
  • [37] R. H. Salih and M. Hasso, A Centre bifurcations of periodic orbits for some special three dimensional systems, Electron. J. Qual. Theory Differ. Equ., 2017(19) (2017), 1-10.
  • [38] R. H. Salih, M. S. Hasso, and S. H. Ibrahim, Centre bifurcations for a three dimensional system with quadratic terms , Zanco j. pure appl. sci., 32(2) (2021), 62-71.
  • [39] B. Sang, Focus quantities with applications to some finite-dimensional systems, Math. Methods Appl. Sci., 44(1) (2021), 464-475.
  • [40] B. Sang and B. Huang, Bautin bifurcations of a financial system, Electron. J. Qual. Theory Differ. Equ., 95 (2017), 1-22.
  • [41] S. K. Tchiedjo, L. K. Kengne, J. Kengne, and G. D. Kenmoe, Dynamical behaviors of a chaotic jerk circuit based on a novel memristive diode emulator with a smooth symmetry control, The European Physical Journal Plus., 137(8) (2022), 940.
  • [42] M. Vijayakumar, H. Natiq, G. D. Leutcho, K. Rajagopal, S. Jafari, and I. Hussain, Hidden and self-excited collective dynamics of a new multistable hyper-jerk system with unique equilibrium, IJBC., 32(05) (2022), 22500630.
  • [43] S. Vaidyanathan, A. S. Kammogne, et al., A Novel 3-D Jerk System, Its Bifurcation Analysis, Electronic Circuit Design and a Cryptographic Application, Electronics (MDPI)., 12(13) (2023), 2818.
  • [44] C. Wang and Q. Ding, A new two-dimensional map with hidden attractors, Entropy, 20(5) (2018), 322.
  • [45] Q. Wang, Z. Tian, X. Wu ,and W. Tan, Coexistence of Multiple Attractors in a Novel Simple Jerk Chaotic Circuit with CFOAs Implementation, Front. Phys., 10 (2022), 835188.
  • [46] C. Wannaboon and T. Masayoshi, An autonomous chaotic oscillator based on hyperbolic tangent nonlinearity, IEEE., (2015), 323-326.
  • [47] A. Wolf, J. B. Swift, H. L. Swinney, and J. A. V. Vastano, Determining lyapunov exponents from a time series, Physica D: nonlinear phenomena, 16(3) (1985), 285-317.
  • [48] S. Yan, J. Wang, and L. Li, Analysis of a New Three-Dimensional Jerk Chaotic System with Transient Chaos and its Adaptive Backstepping Synchronous Control, Integration, (2024), 102210.
آمار
تعداد مشاهده مقاله: 792
تعداد دریافت فایل اصل مقاله: 1,469


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب