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Global dynamics of an exponential system by a discrete-time Lyapunov function
Journal of Taibah University for Science ( IF 3.3 ) Pub Date : 2020-04-15 , DOI: 10.1080/16583655.2020.1746574
A. Q. Khan 1 , H. M. Arshad 1
Affiliation  

In this paper, we explore the boundedness and persistence of positive solution, existence as well as uniqueness of positive equilibrium point, existence of invariant rectangle, local and global dynamics, and rate of convergence of three-directional discrete-time exponential system. Finally, numerical simulations are given to verify not only obtained results but also to have the appearance of stable invariant close curves. The appearance of close curves grantee the fact that the system undergoes a supercritical hopf bifurcation.



中文翻译:

离散时间李雅普诺夫函数对指数系统的整体动力学

本文探讨了正解的有界性和持续性,正平衡点的存在与唯一性,不变矩形的存在,局部和全局动力学以及三方向离散时间指数系统的收敛速度。最后,通过数值模拟不仅验证了所获得的结果,而且还证实了稳定的恒定闭合曲线的出现。闭合曲线的出现使系统经历了超临界Hopf分叉。

更新日期:2020-04-15
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