一类含指数项差分方程模型的分析
Analysis of a Class of Difference Equation Models with Exponential Term
摘要: 本文我们主要研究一类含有指数项的二维差分方程模型的动力学行为。通过计算，我们首先给出了该二维系统不动点的存在性。其次，利用线性部分特征值与稳定性的关系得到了不动点的类型、双曲线不动点的稳定性以及相应的参数条件。最后，结合中心流形定理和分岔理论相关知识讨论了非双曲不动点的分岔现象，从而得到产生flip分岔的条件。
Abstract: In this paper, we mainly study the dynamic behavior of a class of two-dimensional difference equation models with exponential terms. Through calculation, we firstly give the existence of the fixed point of this two-dimensional system. Secondly, the type of fixed point, the stability of the hyperbolic fixed point and the corresponding parameter conditions are obtained by using the relationship between the eigenvalues of the linear part and the stability. Finally, the bifurcation phenomenon of non-hyperbolic fixed point is discussed by combining the knowledge of center manifold theorem and bifurcation theory, and the conditions for generating flip bifurcation are obtained.
文章引用：王容. 一类含指数项差分方程模型的分析[J]. 理论数学, 2022, 12(9): 1493-1500. https://doi.org/10.12677/PM.2022.129163

参考文献

[1] Elettreby, M.F. and El-Metwally, H. (2013) On a System of Difference Equations of an Economic Model. Discrete Dynamics in Nature and Society, 2013, Article ID: 405628.
https://doi.org/10.1155/2013/405628
[2] Khan, A.Q. and Qureshi, M.N. (2016) Stability Analysis of a Discrete Biological Model. International Journal of Biomathematics, 9, Article ID: 1650021.
https://doi.org/10.1142/S1793524516500212
[3] Psarros, N., Papaschinopoulos, G. and Schinas, C.J. (2018) On the Stability of Some Systems of Exponential Difference Equations. Opuscula Mathematica, 38, 95-115.
https://doi.org/10.7494/OpMath.2018.38.1.95
[4] Psarros, N., Papaschinopoulos, G. and Schinas, C.J. (2017) Study of the Stability of a 3Χ3 System of Difference Equations Using Centre Manifold Theory. Applied Mathematics Letters, 64, 185-192.
https://doi.org/10.1016/j.aml.2016.09.002
[5] Dilip, D.S. and Mathew, S.M. (2021) Dynamics of a Second-Order Nonlinear Difference System with Exponents. Journal of the Egyptian Mathematical Society, 29, Article No. 10.
https://doi.org/10.1186/s42787-021-00119-6
[6] Din, Q., Elabbasy, E.M., Elsadany, A.A., et al. (2019) Bifurcation Analysis and Chaos Control of a Second-Order Exponential Difference Equation. Filomat, 33, 5003-5022.
https://doi.org/10.2298/FIL1915003D
[7] Mylona, C., Papaschinopoulos, G. and Schinas, C.J. (2021) Neimark-Sacker, Flip, and Transcritical Bifurcation in a Close to Symmetric System of Difference Equations with Exponential Terms. Mathematical Methods in the Applied Sciences, 44, 10210-10224.
https://doi.org/10.1002/mma.7400
[8] Mylona, C., Papaschinopoulos, G. and Schinas, C.J. (2021) Stability and Flip Bifurcation of a Three Dimensional Exponential System of Difference Equations. Mathematical Methods in the Applied Sciences, 44, 4316-4329.
https://doi.org/10.1002/mma.7031
[9] Carr, J. (1981) Applications of Center Manifold Theory. Springer, New York.
[10] Guckenheimer, J. and Holmes, P. (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York.
https://doi.org/10.1007/978-1-4612-1140-2

为你推荐