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Steven Henry Strogatz (/ ˈ s t r oʊ ɡ æ t s /; born August 13, 1959) is an American mathematician and author, and the Susan and Barton Winokur Distinguished Professor for the Public Understanding of Science and Mathematics at Cornell University.
Steven Strogatz, Non-linear Dynamics and Chaos: With applications to Physics, Biology, Chemistry and Engineering, Perseus Books, 2000. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, 1990.
Download as PDF; Printable version; In other projects ... the dynamics eventually develops chaos. ... Strogatz, Steven (2015). Nonlinear Dynamics and Chaos: With ...
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
Bifurcation theory has been applied to connect quantum systems to the dynamics of their classical analogues in atomic systems, [6] [7] [8] molecular systems, [9] and resonant tunneling diodes. [10] Bifurcation theory has also been applied to the study of laser dynamics [ 11 ] and a number of theoretical examples which are difficult to access ...
In mathematics, the normal form of a dynamical system is a simplified form that can be useful in determining the system's behavior.. Normal forms are often used for determining local bifurcations in a system.
To see how this number arises, consider the real one-parameter map =.Here a is the bifurcation parameter, x is the variable. The values of a for which the period doubles (e.g. the largest value for a with no period-2 orbit, or the largest a with no period-4 orbit), are a 1, a 2 etc.
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
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