Is Chaos Finite? Insights from Nonlinear Damped and Forced Oscillators

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In summary, studies on nonlinear damped and forced oscillators have shown that chaos is finite and ultimately leads to a stable state. These systems exhibit a finite number of chaotic behavior before settling into a predictable pattern. This insight provides a deeper understanding of chaotic systems and their potential for stability.
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Montenegro
Hello there, I am a new member, my name is Javier Montenegro Joo, work at VirtualDynamicsSoft, I am a computational & simulational physicist.Due to the literature around us (papers, books), until some months ago I used to believe chaotic events had no end once they started. I also believed chaotic events where every time stronger once they started.

Until I wrote a simulation computer program to study chaos in the nonLinear damped and forced oscillator (NLDFO), this model may be considered the drosophila (fruit fly) of chaos, because it allows to study chaos almost intuitively.

As a result of my computer simulations I encountered that chaos is finite, it has a beginning and an end, and chaotic events may be multiple. These results are in opposition to what physicist were accustomed to think but never talked about, maybe because computational studies were always limited to a few hundreds time-steps, my simulations run from 1 million to 30 million time-steps.

Two referees at the physics journal where I have submitted a paper declared this was an original research, and the results will appear soon.

Though my results are from the NLDFO they shed light on the behaviour we must expect in other chaotic systems. I have also encountered that the velocity during a chaotic event also displays a bifurcation cascade.

Those people curious about the above exposed may see two publications I made in the university where I teach, these papers are in Research Gate and the links are:

(1) https://www.researchgate.net/publication/280716284_Multiplicity_and_transitoriness_of_chaotic_events?ev=prf_pub

(2) https://www.researchgate.net/publication/288838669_Structure_of_the_Velocity_during_a_Chaotic_Episode JMJ
 
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  • #2
Welcome to PF Javier!
 

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