This article is devoted to the study of chaos and bifurcation in the real dynamics of a newly proposed two-parameter family of transcendental functions. We assume that one parameter is continuous and other parameter is discrete. For certain parameters, the theoretical computations of the real fixed points of a family of functions are given. The numerical simulations of the real periodic points of functions are described. The bifurcation diagrams of the real dynamics of these functions for some selected parameter values are provided. In these bifurcation diagrams, the period-doubling occurs which proceeds to a pathway toward chaos in the dynamics of functions. Further, the periodic-three window is visible in the bifurcation diagrams which implies chaos. Lastly, chaos is quantified in the dynamics of functions by calculating Lyapunov exponents. KeywordsBifurcation, Chaos, Dynamics, Fixed points, Lyapunov exponents, Periodic points.

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与指数映射相关的先验函数两参数族中的混沌行为

本文致力于研究新提出的先验函数的两参数族的真实动力学中的混沌和分叉。我们假设一个参数是连续的，而另一个参数是离散的。对于某些参数，给出了一系列函数的实际不动点的理论计算。描述了函数的真实周期点的数值模拟。提供了针对某些选定参数值的这些功能的实际动力学的分叉图。在这些分叉图中，发生了周期倍增，该周期倍增通向功能动力学中的混沌路径。此外，在分叉图中可见周期3窗口，这意味着混乱。最后，通过计算李雅普诺夫指数来量化函数动力学中的混沌。