一类 Filippov 型 Faraday 模型的分岔与混沌动力学分析

Abstract

Abstract:

The stability of the Faraday model and its bifurcation and chaos phenomena under the threshold control strategy are deeply analyzed, and a class of three-dimensional Filippov-type Faraday models is established. The existence and stability of the equilibrium points of the two subsystems are investigated by using the qualitative technique of nonsmooth dynamical systems. The stability of the equilibrium point and the set of bifurcations in the sliding vector field are also investigated, revealing rich dynamical behaviors including multiplicative bifurcations, sliding bifurcations, and crossing bifurcations. This study can be widely applied to various kinds of power generation equipment and energy management systems, providing theoretical support for realizing more efficient and intelligent energy management.

Key words: Filippov-type system, Faraday model, threshold control strategy, sliding bifurcation, chaos

CLC Number:

O175.14

Yushan Xi, Jicheng Duan, Rongsan Chen, Haijun Xiao. Sliding Bifurcation and Complex Dynamics Analysis of a Class of Filippov-Type Faraday Model[J].Acta mathematica scientia,Series A, 2025, 45(5): 1616-1631.

Trendmd

References

[1]	Zheng Y, Chen X. Degenerate T-singularity bifurcation and crossing periodic orbits in a 3-dimensional piecewise smooth system. Journal of Differential Equations, 2023, 354: 296-324
[2]	Wang F, Wei Z, Zhang W. Sliding homoclinic orbits and chaotic dynamics in a class of 3D piecewise-linear Filippov systems. Nonlinear Dynamics, 2024, 112(22): 20461-20481
[3]	Huang L, Wang J. Global dynamics of piecewise smooth systems with switches depending on both discrete times and status. SIAM Journal on Applied Dynamical Systems, 2024, 23(3): 2533-2556
[4]	Filippov A F. Differential equations with discontinuous right-hand side. Matematicheskii Sbornik, 1960, 93(1): 99-128
[5]	Bernardo M, Budd C, Champneys A R, et al. Piecewise-Smooth Dynamical Systems:Theory and Apxinplications. Berlin: Springer Science, 2008
[6]	杨静, 柯昌成, 魏周超. 一类连续和不连续分段线性系统的周期解研究. 数学物理学报, 2021, 41A(4): 1053-1065
[6]	Yang J, Ke C C, Wei Z C. A study of periodic solutions for a class of continuous and discontinuous piecewise linear systems. Acta Math Sci, 2021, 41A(4): 1053-1065
[7]	Wei Z, Li Y, Moroz I, et al. Melnikov-type method for a class of planar hybrid piecewise-smooth systems with impulsive effect and noise excitation: Heteroclinic orbits. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32(10): Art 103127
[8]	Wang F, Wei Z, Zhang W, et al. Coexistence of three heteroclinic cycles and chaos analyses for a class of 3D piecewise affine systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023, 33(2): Art 023108
[9]	Duan J, Wei Z, Li G, et al. Strange nonchaotic attractors in a class of quasiperiodically forced piecewise smooth systems. Nonlinear Dynamics, 2024, 112(14): 12565-12577
[10]	Yang Q, Huang Y. Chaotic Dynamics arising from sliding heteroclinic cycles in 3D Filippov systems. International Journal of Bifurcation and Chaos, 2023, 33(1): Art 2350009
[11]	Hamdallah S A A, Arafa A A, Tang S, et al. Complex dynamics of a Filippov three-species food chain model. International Journal of Bifurcation and Chaos, 2021, 31(5): Art 2150074
[12]	Zhou W, Zhao T, Wang A, et al. Bifurcations and dynamics of a Filippov epidemic model with nonlinear threshold control policy and medical-resource constraints. Chaos Solitons & Fractals, 2024, 184: Art 114992
[13]	Zhou H, Tang S. Complex dynamics and sliding bifurcations of the Filippov Lorenz-Chen system. International Journal of Bifurcation and Chaos, 2022, 32(12): Art 2250182
[14]	Deng Q, Wang C, Lin H. Chaotic dynamical system of Hopfield neural network influenced by neuron activation threshold and its image encryption. Nonlinear Dynamics, 2024, 112(8): 6629-6646
[15]	Mohammadi H, Challenor P, Goodfellow M. Emulating complex dynamical simulators with random Fourier features. SIAM/ASA Journal on Uncertainty Quantification, 2024, 12(3): 788-811
[16]	Wu F, Xi F, Zhu C. On a class of McKean-Vlasov stochastic functional differential equations with applications. Journal of Differential Equations, 2023, 371: 31-49
[17]	Hide R, Skeldon A C, Acheson D J. A study of two novel self-exciting single-disk homopolar dynamos: theory. Proceedings of the Royal Society of London, 1996, 452(1949): 1369-1395
[18]	Brandenburg A, Ntormousi E. Galactic dynamos. Annual Review of Astronomy and Astrophysics, 2023, 61(1): 561-606
[19]	Foldes R, Lévêque E, Marino R, et al. Efficient kinetic Lattice Boltzmann simulation of three-dimensional Hall-MHD turbulence. Journal of Plasma Physics, 2023, 89(4): Art 905890413
[20]	方秀珍, 彭爱武, 刘保林. 盘式磁流体发电机通道结构对等离子体稳定性的影响研究. 电工电能新技术, 2020, 39(9): 13-19
[20]	Fang X Z, Peng A W, Liu B L. A study of the effect of disk magnetohydrodynamic generator channel structure on plasma stability. Advanced Technology of Electrical Engineering and Energy, 2020, 39(9): 13-19
[21]	Galvan-Ruiz J L, Sellschopp-Sanchez F S, Rivero M, et al. Theoretical, numerical and experimental investigation of a Faraday disc generator for energy harvesting applications. IEEE Latin America Transactions, 2023, 21(7): 849-857
[22]	Patrinos K. On the Unipolar generator: An experimental and theoretical study. Journal of Applied Mathematics and Physics, 2024, 12(8): 2928-2958
[23]	Galvan-Ruiz J L, Sellschopp-Sanchez F S, álvarez-Macías C, et al. Theoretical and experimental investigation of a Faraday disc generator//2022 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC). IEEE, 2022, 6: 1-6
[24]	Moroz I M. The Hide, Skeldon, Acheson dynamo revisited. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007, 463(2077): 113-130
[25]	Cristiano R, Carvalho T, Tonon D J, et al. Hopf and homoclinic bifurcations on the sliding vector field of switching systems in R3. Nonlinear Phenomena, 2017, 347: 12-20
[26]	Kuznetsov Y A, Rinaldi S, Gragnani A. One-parameter bifurcations in planar Filippov systems. International Journal of Bifurcation and Chaos, 2003, 13(8): 2157-2188
[27]	Wang A, Xiao Y, Smith R. Multiple equilibria in a nonsmooth epidemic model with medical resource constraints. Bulletin of Mathematical Biology, 2019, 81(4): 963-994
[28]	DeJesus E X, Kaufman C. Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Physical Review A, 1987, 35(12): Art 5288
[29]	Moroz I M. Template analysis of a Faraday disk dynamo. The European Physical Journal Special Topics, 2008, 165(1): 211-220

Sliding Bifurcation and Complex Dynamics Analysis of a Class of Filippov-Type Faraday Model

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0

[1]	Yongjian Liu,Qiujian Huang. Jacobi Analysis of the Rabinovich System [J]. Acta mathematica scientia,Series A, 2021, 41(3): 783-796.
[2]	Liheng Sang,Zhenlong Chen,Xiaozhen Hao. Smoothness for the Renormalized Self-Intersection Local Time of Bifractional Brownian Motion [J]. Acta mathematica scientia,Series A, 2020, 40(3): 796-810.
[3]	Heyuan Wang. Dynamical Mechanism and Energy Evolution of a Five-Modes System of the Navier-Stokes Equations For a Two-Dimensional Incompressible Fluid on a Torus [J]. Acta mathematica scientia,Series A, 2020, 40(2): 315-327.
[4]	Heyuan Wang. Dynamical Mechanism and Energy Conversion of Couette-Taylor Flow [J]. Acta mathematica scientia,Series A, 2020, 40(1): 243-256.
[5]	Zhi Wang,Litan Yan,Xianye Yu. Local Times of the Solution to Stochastic Heat Equation with Fractional Noise [J]. Acta mathematica scientia,Series A, 2019, 39(3): 582-595.
[6]	Wang Jianjun. On the Invariance of Maximal Distributional Chaos of Weighted Shift Operators on ∑(X) [J]. Acta mathematica scientia,Series A, 2018, 38(3): 446-453.
[7]	Yao Yuwu, Chen Xiu, Niu Xin. Distributional Chaos on Complex Sectors [J]. Acta mathematica scientia,Series A, 2017, 37(5): 950-961.
[8]	Wang Heyuan, Cui Jin. The Analysis of Global Stability and Numerical Simulation of Chaos Behaviors of Rotating Flow [J]. Acta mathematica scientia,Series A, 2017, 37(4): 783-792.
[9]	Yang Jihua, Zhang Erli, Liu Mei. Dynamic Analysis and Chaos Control of a Finance System with Delayed Feedbacks [J]. Acta mathematica scientia,Series A, 2017, 37(4): 767-782.
[10]	Wu Xinxing. A Remark on the Weak Specification Property [J]. Acta mathematica scientia,Series A, 2017, 37(4): 601-606.
[11]	Wang Heyuan. The Dynamical Behaviors and the Numerical Simulation of a Five-Mode Lorenz-Like System of the MHD Equations for a Two-Dimensional Incompressible Fluid on a Torus [J]. Acta mathematica scientia,Series A, 2017, 37(1): 199-216.
[12]	Wu Xinxing, Wang Jianjun. Some Remarks on P-Minimal Dynamical Systems [J]. Acta mathematica scientia,Series A, 2016, 36(5): 879-885.
[13]	Lu Tianxiu, Zhu Peiyong, Wu Xinxing. Distributional Chaos in Nonautonomous Discrete Systems [J]. Acta mathematica scientia,Series A, 2015, 35(3): 558-566.
[14]	HU Han-Ping, LIU Shuang-Hong, WANG Zu-Xi, Wu Xiao-Gang. A Chaotic Poly phase Pseudorandom Sequence [J]. Acta mathematica scientia,Series A, 2004, 24(2): 251-256.
[15]	Zhang Jianfeng, Xie Xiangdong. Weak Transverse and Weak Chaos [J]. Acta mathematica scientia,Series A, 1998, 18(3): 241-245.