一个变形耦合电机模型的不变代数曲面（英文）
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摘要
考虑两种损耗特性的耦合电机模型,可由一个三维非线性自治方程组表示,该模型最近由郝建红等提出,其展示了非常复杂的动力学行为.从动力系统的可积性角度研究了该系统的可积性,用解线性偏微分方程的特征曲线法,求出了系统具有不变代数曲面的所有参数条件.
A coupled dynamos model considering two loss characteristics can be described as a threedimensional nonlinear autonomous system proposed recently by HAO et al,which exhibits very complicated dynamics.In this paper,invariant algebraic surfaces of this system are investigated from the view of integrability.Using the method of characteristic curves for solving linear partial differential equations,we obtain the parameter conditions when the system has invariant algebraic surfaces.
A coupled dynamos model considering two loss characteristics can be described as a threedimensional nonlinear autonomous system proposed recently by HAO et al,which exhibits very complicated dynamics.In this paper,invariant algebraic surfaces of this system are investigated from the view of integrability.Using the method of characteristic curves for solving linear partial differential equations,we obtain the parameter conditions when the system has invariant algebraic surfaces.
引文
[1]ZHANG X.Integrability of Dynamical Systems:Algebra and Analysis[M].Singapore:Springer Nature,2017.
[2]MA W.A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems[J].Applied Mathematics and Mechanics,1992,13(4):369-377.
[3]YIN J,FAN Y,ZHANG J,et al.Some new integrable nonlinear dispersive equations and their solitary wave solutions[J].Acta Physica Sinica,2011,60(8):7-10.
[4]ZHANG X.Liouvillian integrability of polynomial differential systems[J].Transactions of the American Mathematical Society,2016,368(1):607-622.
[5]ZHANG X.Local first integrals for systems of differential equations[J].Journal of Physics A:Mathematical and General,2003,36(49):12243-12253.
[6]LU T,ZHANG X.Darboux polynomials and algebraic integrability of the Chen system[J].International Journal of Bifurcation and Chaos,2007,17(8):2739-2748.
[7]LLIBRE J,ZHANG X.Invariant algebraic surfaces of the Rikitake system[J].International Journal of Bifurcation and Chaos,2000,33(42):7613-7635.
[8]FERRAGUT A,VALLS C.On the complete integrability of the Raychaudhuri differential system in R4 and of a CRNT model in R~5[J].Qualitative Theory of Dynamical Systems,2018,17(1):291-307.
[9]FERRAGUT A,VALLS C,WIUF C.On the Liouville integrability of Edelstein reaction system in R~3[J].Chaos Solitons and Fractals,2018,108:129-135.
[10]HAO J,SUN N.The characteristics of the chaotic parameters for a loss type of modified coupled dynamic system[J].Acta Physica Sinica,2012,61(15):64-72.
[11]WANG X,WU X.Chaos control of a modified coupled dynamos system[J].Acta Physica Sinica,2007,21(26):4593-4610.
[12]WU S,SUN Y,HAO J,et al.Bifurcation and dual-parameter characteristic of the coupled dynamos system[J].Acta Physica Sinica,2011,60(1):84-92.
[2]MA W.A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems[J].Applied Mathematics and Mechanics,1992,13(4):369-377.
[3]YIN J,FAN Y,ZHANG J,et al.Some new integrable nonlinear dispersive equations and their solitary wave solutions[J].Acta Physica Sinica,2011,60(8):7-10.
[4]ZHANG X.Liouvillian integrability of polynomial differential systems[J].Transactions of the American Mathematical Society,2016,368(1):607-622.
[5]ZHANG X.Local first integrals for systems of differential equations[J].Journal of Physics A:Mathematical and General,2003,36(49):12243-12253.
[6]LU T,ZHANG X.Darboux polynomials and algebraic integrability of the Chen system[J].International Journal of Bifurcation and Chaos,2007,17(8):2739-2748.
[7]LLIBRE J,ZHANG X.Invariant algebraic surfaces of the Rikitake system[J].International Journal of Bifurcation and Chaos,2000,33(42):7613-7635.
[8]FERRAGUT A,VALLS C.On the complete integrability of the Raychaudhuri differential system in R4 and of a CRNT model in R~5[J].Qualitative Theory of Dynamical Systems,2018,17(1):291-307.
[9]FERRAGUT A,VALLS C,WIUF C.On the Liouville integrability of Edelstein reaction system in R~3[J].Chaos Solitons and Fractals,2018,108:129-135.
[10]HAO J,SUN N.The characteristics of the chaotic parameters for a loss type of modified coupled dynamic system[J].Acta Physica Sinica,2012,61(15):64-72.
[11]WANG X,WU X.Chaos control of a modified coupled dynamos system[J].Acta Physica Sinica,2007,21(26):4593-4610.
[12]WU S,SUN Y,HAO J,et al.Bifurcation and dual-parameter characteristic of the coupled dynamos system[J].Acta Physica Sinica,2011,60(1):84-92.