Applications of Lambert-Tsallis and Lambert-Kaniadakis Functions in Differential and Difference Equations with Deformed Exponential Decay

TL;DR

This paper explores the application of Lambert-Tsallis and Lambert-Kaniadakis functions to analyze differential and difference equations with deformed exponential decay, revealing their utility in studying chaotic dynamics and projectile motion.

Contribution

It introduces the use of deformed Lambert functions in analyzing systems with Tsallis and Kaniadakis exponentials, providing new tools for stability and motion analysis.

Findings

Stable behavior of logistic map with deformed exponential decay identified.

Range of projectile calculated using Lambert-Tsallis function.

Insights into dynamics of systems with non-linear differential equations.

Abstract

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.