Lambert-Tsallis和Lambert-Kaniadakis函数在变形指数衰减微分方程和差分方程中的应用
Applications of Lambert-Tsallis and Lambert-Kaniadakis Functions in Differential and Difference Equations with Deformed Exponential Decay
摘要：
分析由微分（连续情形）或差分方程（离散情形）建模的具有变形指数衰减的动力系统，这里我们考虑Tsallis和Kaniadakis指数，可能需要使用最近提出的变形Lambert函数：Lambert-Tsallis和Lambert-Kaniadakis函数。在这个方向上，目前的工作研究了变形指数衰减的Logistic映射，使用Lambert-Tsallis和Lambert-Kaniadakis函数，以确定稳定的行为和动力学的弱混沌制度的熵。此外，我们还研究了垂直运动由一个二阶导数系数为Tsallis指数的非线性微分方程控制时的抛体运动。在这种情况下，我们使用Lambert-Tsallis函数计算了射弹的射程。
英文摘要：
The analysis of a dynamical system modelled by differential (continuum case) or difference equation (discrete case) with deformed exponential decay, here we consider Tsallis and Kaniadakis exponentials, may require the use of the recently proposed deformed Lambert functions: the Lambert-Tsallis and Lambert-Kaniadakis functions. In this direction, the present work studies the logistic map with deformed exponential decay, using the Lambert-Tsallis and the Lambert-Kaniadakis functions to determine the stable behaviour and the dynamic of the disentropy in the weak chaotic regime. Furthermore, we investigate the motion of projectile when the vertical motion is governed by a non-linear differential equation with Tsallis exponential in the coefficient of the second order derivative. In this case, we calculated the range of the projectile using the Lambert-Tsallis function.
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