Download PDF by Frank C. Hoppensteadt: Analysis and Simulation of Chaotic Systems (2nd Edition)

Download PDF by Frank C. Hoppensteadt: Analysis and Simulation of Chaotic Systems (2nd Edition)

By Frank C. Hoppensteadt

ISBN-10: 1475773862

ISBN-13: 9781475773866

Starting with practical mathematical or verbal versions of actual or organic phenomena, the writer derives tractable versions for extra mathematical research or machine simulations. For the main half, derivations are according to perturbation tools, and nearly all of the textual content is dedicated to cautious derivations of implicit functionality theorems, the strategy of averaging, and quasi-static kingdom approximation equipment. The duality among balance and perturbation is constructed and used, depending seriously at the suggestion of balance less than chronic disturbances. proper themes approximately linear platforms, nonlinear oscillations, and balance tools for distinction, differential-delay, integro-differential and usual and partial differential equations are built during the booklet. For the second one variation, the writer has restructured the chapters, putting specified emphasis on introductory fabrics in Chapters 1 and a couple of as specific from presentation fabrics in Chapters three via eight. additionally, extra fabric on bifurcations from the viewpoint of canonical versions, sections on randomly perturbed structures, and a number of other new desktop simulations were additional.

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Additional info for Analysis and Simulation of Chaotic Systems (2nd Edition)

Example text

In this case, small perturbations of the pendulum from the straight up position die out, approximately like exp(−rt/2). shows that an oscillating environment can stabilize a static state that is unstable without oscillation. This is an important phenomenon found in many physical and biological systems [1, 87, 127]. 5 Fourier Methods No result comparable to Floquet’s Theorem is available for systems having almost periodic coefficients. However, when these systems do arise in applications, they can be studied using generalized Fourier methods.

In the next section we show how some other models can be transformed into phase-amplitude coordinates, but in this section we consider systems of (angular) phase equations. In general, these models are measured by an 36 2. 6. An annular region that is invariant to solutions of Lienard’s equation. observable, say F (x1 , . . , xN ), which is 2π-periodic in each of the phases x1 , . . , xN . Because of this, we need only consider these variables in a set T N = {(x1 , . . , xN ) : 0 ≤ xj < 2π for j = 1, .

1). In the other case, it is an unstable node. 2. The roots are real and have opposite signs. 2). 2). 3. The roots are complex conjugates. If the real part of the eigenvalues is negative, then all solutions spiral into the critical point. 3). If the real part is positive, solutions spiral away from the critical point. This is an unstable spiral or a spiral source. 4). 4 is also seen in nonlinear systems. However, nonlinear systems can have more complicated behavior. 2 Poincar´e and Bendixson’s Theory Consider a system of two ordinary differential equations of the form dx dt dy dt = f (x, y) = g(x, y), 30 2.

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Analysis and Simulation of Chaotic Systems (2nd Edition) by Frank C. Hoppensteadt


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