Amazing behavior and transition to chaos of some sequences using Collatz like problems and Quibic duffing

TL;DR

This paper explores complex behaviors and chaos transitions in discrete maps and the driven cubic-quintic Duffing system, employing Collatz-like problems and advanced theories in number theory and dynamical systems.

Contribution

It introduces a novel theoretical approach to predict limit cycles and suppress chaos in damped driven systems using Collatz-like sequences.

Findings

Predicted the number of limit cycles around equilibrium points.

Developed a method for chaos suppression in driven systems.

Presented new results on the behavior of Collatz-like sequences.

Abstract

In this paper we shall show amazing behavior of some discrete maps using Collatze like problems and some advanced theories in analytic number theory and dynamical system,we have investigated the driven cubic-quintic Duffing equation such that , We were able to predict the number of limit cycles around the equilibrium and to develop a theoretical approach to chaos suppression in damped driven systems using Collatze like problem sequences , some new results regarding behavior of that sequence are presented.