What we called for a phenomenon when a system has chaotic behaviour for parameter ppc it has transient chaotic behaviour?
Doesn't chaos occurs in nonlinear and dynamic systems? They are always coupled.
Hi,
If the behavior of a system changes with the variation of a parameter, we call "bifurcation". Bifurcation constitutes different cases including the change in the number of equilibrium points, behavior of these points, apearing limit cycle, or exhibiting chaotic phenomenon.
See the book: Nonlinear systems, hassan khalil.
The parameters you're referring to were, and still often are, called crises. However, these parameters of qualitative change in chaotic behavior are plentiful, and the diversity depends on the maps studied, so most authors reserve the term "crises" for a subset of these, definition depending on author. My response is stemmed from complex Dynamics, (where I feel pretty well-behaved); perhaps, this is not exactly what you are asking (but I'm pretty sure it is). In complex Dynamics, such parameters are not even close to being fully classified (internal crisis points, cusps, tips, cascading limits, Misirewich points, singular parameters, etc.... I'm sure I misspelled M-points). Search for crises, primitive roots, Feingenbaum point, the MLC conjecture. Sorry for the probable misspellings of names (I was never a fan of mathematical phenomena, tools, theorems and such named after people, short of Reimann and Klein...😛)
@ Ross Flek
Thank you ,Sir.
Your valuable answer is really helpful.
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