دورات النهائية من النظام التفاضلي ثلاثي الأبعاد التربيعية عن طريق تشعب هوبف

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Gasull A, Giacomini H. Number of Limit Cycles for Planar Systems with Invariant Algebraic Curves. Qual Theory Dyn Syst. 2023; 22(2): 44. https://doi.org/10.1007/s12346-023-00746-7

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Musafirov E, Grin A, Pranevich A, Munteanu F, Şterbeţi C. 3D Quadratic ODE Systems with an Infinite Number of Limit Cycles. In International Conference on Applied Mathematics and Numerical Methods – fourth edition (ICAMNM 2022). ITM Web Conf. 2022; 49: 02006. https://doi.org/10.1051/itmconf/20224902006

Llibre J, Martínez YP, Valls C. Limit Cycles Bifurcating of Kolmogorov Systems in R2 and in R3. Commun Nonlinear Sci Numer Simul. 2020; 91: 105401. https://doi.org/10.1016/j.cnsns.2020.105401

Sánchez-Sánchez I, Torregrosa J. Hopf Bifurcation in 3-dimensional Polynomial Vector Fields. Commun Nonlinear Sci Numer Simul. 2022;105: 106068. https://doi.org/10.1016/j.cnsns.2021.106068

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Dias FS, Mello LF. Non-Linear Differential Systems in the 3–Space: A Note on Periodic Solutions by the Analysis of Two Examples. Math Methods Appl Sci. 2020; 43(7):4383-90. https://doi.org/10.1002/mma.6199

Wei Z, Yang Q. Anti-Control of Hopf Bifurcation in the New Chaotic System with Two Stable Node-Foci. Appl Math Comput. 2010; 217(1): 422-429. https://doi.org/10.1016/j.amc.2010.05.035

Huang W, Wang Q, Chen A. Hopf Bifurcation and the Centers on Center Manifold for a Class of Three‐Dimensional Circuit System. Math Methods Appl Sci. 2020; 43(4): 1988-2000. https://doi.org/10.1002/mma.6026

Llibre J, Zhang, X. Hopf Bifurcation in Higher Dimensional Differential Systems via the Averaging Method. Pac J Math. 2009; 240(2): 321-341. https://doi.org/10.2140/pjm.2009.240.321

Yu P, Han M. Ten Limit Cycles Around a Center-Type Singular Point in a 3-D Quadratic System with Quadratic Perturbation. Appl Math Lett. 2015; 44: 17-20. http://dx.doi.org/10.1016/j.aml.2014.12.010

Yuri A. Kuznetsov. Elements of Applied Bifurcation Theory. 4th edition. Applied Mathematical Sciences (AMS, volume 112). Springer Cham. 19 April 2023; XXVI: 703p. https://doi.org/10.1007/978-3-031-22007-4.

Sotomayor J, Mello LF, Braga DD. Bifurcation Analysis of the Watt Governor System. Comput Appl Math. 2007; 26(1): 19-44.

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Atiya AN, Hassan HES, Ibrahim KE, ElGhandour OM, Tolba MF. Generalized Formula for Generating N-Scroll Chaotic Attractors. In 2020 2nd Novel Intelligent and Leading Emerging Sciences Conference (NILES), Giza, Egypt. IEEE. 2020 Oct 24; 492-496. https://doi.org/10.1109/NILES50944.2020.9257932

Zhang X, Li C. A Novel Type of Chaotic Attractor with a Multiunit Structure: From Multiscroll Attractors to Multi-bond Orbital Attractors. Eur Phys J Plus. 2022 Sep 15; 137(9): 1048. https://doi.org/10.1140/epjp/s13360-022-03268-4

Altun K. Multi-Scroll Attractors with Hyperchaotic Behavior Using Fractional-Order Systems. J Circuits Syst Comput. 2022 Mar 30; 31(05): 2250085. https://doi.org/10.1142/S0218126622500852

Sugandha K, Singh PP. Generation of a Multi-Scroll Chaotic System via Smooth State Transformation. J Comput Electron. 2022 Aug; 21(4): 781-91. https://doi.org/10.1007/s10825-022-01892-y

Tlelo-Cuautle E, Guillén-Fernández O, de Jesus Rangel-Magdaleno J, Melendez-Cano A, Nuñez-Perez JC, de la Fraga LG. Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications. Academic Press; 2019 Jan 1. Chap 15, FPGA implementation of chaotic oscillators, their synchronization, and application to secure communications:301-328. https://doi.org/10.1016/B978-0-12-815838-8.00015-7

Al-Bahrani EA, Kadhum RN. A New Cipher Based on Feistel Structure and Chaotic Maps. Baghdad Sci J. 2019 Jan 2; 16(1(Suppl.)): 270-80. https://doi.org/10.21123/bsj.2019.16.1(Suppl.).0270

Mazher AN, Waleed J. Retina Based Glowworm Swarm Optimization for Random Cryptographic Key Generation. Baghdad Sci J. 2022 Feb 1; 19(1): 0179. https://doi.org/10.21123/bsj.2022.19.1.0179

Çiçek S. The Effect of Using Multi-Scroll Chaotic Systems on Chaos-Based Random Number Generators’ Performance. J Circuits Syst Comput. 2022 Oct 16; 31(15): 2250259. https://doi.org/10.1142/S0218126622502590

Nasr S, Mekki H, Bouallegue K. A Multi-Scroll Chaotic System for a Higher Coverage Path Planning of a Mobile Robot Using Flatness Controller. Chaos, Solitons & Fractals. 2019; 118: 366-75. https://doi.org/10.1016/j.chaos.2018.12.002

Elhadj Z, Sprott JC. Simplest 3D Continuous-Time Quadratic Systems as Candidates for Generating Multiscroll Chaotic Attractors. Int J Bifurc Chaos Appl. 2013 Jul; 23(07): 1-6. https://doi.org/10.1142/S0218127413501204

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