@@CatSynthTV Thank you for your reply. I asked you that question because I am trying to understand eventual connection between exponential rate of change and Feigenbaum first constant. Doesn't the Feigenbaum first constant express ratio in bifurcation diagram, where the evolution of a dynamic system increases its complexity exponentially, leading to periodical chaos?
Yes, the period doubling has a nearly exponential rate increase, which is why it converges to a specific boundary for the onset of chaos. So you are correct 😺
@@CatSynthTV Let me ask you one more question, please. Is there any reason why a mathematical expression of a physical process based on an exponential rate of change would include the first Feigenbaum constant?
Hi. The quadratic logistic map relates the derivative of the logistic function in population modules. If L is the logistic function then dL/dx = aL (1 - L). The right-hand side is the quadric function. If you treat that function as a map repeatedly applied to its output, you get the logistic map. Hope this helps. Please let me know if you have further questions and I will try my best to answer 😺
Thank you for such a clear explanation
You are most welcome! 😺
Really lovely explanation and I enjoy your enthusiasm. Thanks!
Thanks! Glad you enjoyed the video 😺
Fascinating! Thank you!
Excellent work!
Thank you! Cheers! 😺
CatSynth TV - Does Feigenbaum first constant have anything to do with exponential rate of change?
Period doubling described by the Feigenbaum constant and exponential rate of change are different, though they both involve proportionality.
@@CatSynthTV Thank you for your reply. I asked you that question because I am trying to understand eventual connection between exponential rate of change and Feigenbaum first constant. Doesn't the Feigenbaum first constant express ratio in bifurcation diagram, where the evolution of a dynamic system increases its complexity exponentially, leading to periodical chaos?
Yes, the period doubling has a nearly exponential rate increase, which is why it converges to a specific boundary for the onset of chaos. So you are correct 😺
@@CatSynthTV Thank you :)
@@CatSynthTV Let me ask you one more question, please. Is there any reason why a mathematical expression of a physical process based on an exponential rate of change would include the first Feigenbaum constant?
Awesome, Can I get MatLab codes for this? Thanks
Thanks! I my coding for this in Swift, Python, and GNUPlot’s language. I’m sure MatLab versions exist.
Great video thank you so much :)
Thank you and glad you enjoyed it 😺
Yay for chaos!
I’m struggling with the translation from logistic models and the quadratic of the logistic map
Hi. The quadratic logistic map relates the derivative of the logistic function in population modules. If L is the logistic function then dL/dx = aL (1 - L). The right-hand side is the quadric function. If you treat that function as a map repeatedly applied to its output, you get the logistic map.
Hope this helps. Please let me know if you have further questions and I will try my best to answer 😺
@@CatSynthTV I feel like I’m almost there. But I need to explain to me over and over again by different people.
@@CatSynthTV tysm
You're welcome 😺
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Why not? 😸
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For one logistic system we change our life we are stupid