منابع مشابه
Dynamical Systems and Chaos
These are some notes related to the one-semester course Math 5535 Dynamical Systems and Chaos given at the University of Minnesota during Fall 2012 with an emphasis to the study of continuous and discrete dynamical systems of dimension one and two. An ambitious list of topics to be covered include phase portraits, fixed points, stability, bifurcations, limit sets, periodic orbit, Poincaré map a...
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In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics and control theory, and focussing on qualitative theory. From this perspective we show how concepts of stability enable us to classify dynamical equations and...
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In very general terms, we call DYNAMICAL any kind of “system” which evolves in time, starting from an initial time t0, and whose state at any later time t > t0 can be explicitly and uniquely determined from the assumed knowledge of its initial state at t = t0. One of the major goals of the theory of dynamical systems it to understand how the evolution of any such system is determined by its ini...
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In the investigations of chaos in dynamical systems a major role is played by symbolic dynamics, i.e. the description of the system by a shift on a symbol space via conjugation. We examine whether any kind of noise can strengthen the stochastic behaviour of chaotic systems dramatically and what the consequences for the symbolic description are. This leads to the introduction of random subshifts...
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Much of engineering is concerned with the topic of optimization, and at the heart of much of our optimization is dynamical systems. Dynamical systems can be thought of as either non-linear continuous-time differential equations or difference equations. Chaos occurs in dynamical systems, and frequently in engineering we seek to avoid chaos. At times chaos becomes the central fascination. This pa...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1988
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270002712x