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alberacca / Lyapunov-spectrum

Fast jacobian-free computation of the first m largest lyapunov exponents and Kaplan-Yorke dimension of dynamical systems.
MIT License
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Problems concerning the calculation of lyapunov dimension of delay differential equations #2

Open yoga-Yuki opened 1 year ago

yoga-Yuki commented 1 year ago

Hello! Your code is very clear, but I have a problem when using your project to calculate the Lyapunov dimension of Mackey-glass system, because the state of Mackey-glass system depends on the state before the delay, meanwhile, Lorenz system has 3 degrees of freedom, The Mackey-glass system has only one variable describing its evolution. How can I use your code to calculate the Lyapunov dimension of the Mackey-glass system? Your code is very clear, but I have a problem when using your project to calculate the Lyapunov dimension of Mackey-glass system, because the state of Mackey-glass system depends on the state before the delay, meanwhile, Lorenz system has 3 degrees of freedom, The Mackey-glass system has only one variable describing its evolution. How can I use your code to calculate the Lyapunov dimension of the Mackey-glass system?

alberacca commented 1 year ago

Hi! I have no direct experience with time delayed systems, but, if the Lyapunov exponents are defined in the same way of ordinary differntial equations, you need to to swap the integrator and system functions with a solver of the Mackey-glass system. I.e., something that advances the equations in time. You would need also to change the number of dimensions of the system and the number of Lyapunov exponents that you want to compute accordingly.

yoga-Yuki commented 1 year ago

Thank you for your reply, maybe my understanding of Lyapunov exponent is not quite complete, I also looked up relevant literature about how to calculate the Lyapunov exponent of delayed differential equation is very little, even if there is, it only gives a simple concept. I think it is really a little difficult for me to use code to implement, thank you again for your reply.