By Steven H. Strogatz

Filenote: PDF retail from EBL. appears to be like Westview/EBL have created it through taking their great epub and switched over to PDF + pagination instead of the common appealing PDF imprint.
Publish yr note: First released in 1994 (first edition)
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This textbook is geared toward newbies to nonlinear dynamics and chaos, particularly scholars taking a primary direction within the topic. The presentation stresses analytical equipment, concrete examples, and geometric instinct. the idea is constructed systematically, beginning with first-order differential equations and their bifurcations, through section aircraft research, restrict cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, interval doubling, renormalization, fractals, and weird attractors.

A precise characteristic of the publication is its emphasis on purposes. those contain mechanical vibrations, lasers, organic rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic regulate platforms, chaotic waterwheels, or even a strategy for utilizing chaos to ship mystery messages. In each one case, the medical heritage is defined at an uncomplicated point and heavily built-in with mathematical theory.

In the two decades because the first variation of this publication seemed, the tips and strategies of nonlinear dynamics and chaos have chanced on software to such interesting new fields as structures biology, evolutionary online game conception, and sociophysics. This moment version comprises new routines on those state-of-the-art advancements, on subject matters as different because the curiosities of visible conception and the tumultuous love dynamics in long past With the Wind.

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Extra info for Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (2nd Edition) (Studies in Nonlinearity)

Example text

1). We see that the fixed point x* = 0 is very unstable—the slope f ′(0) is infinite. Chastened by this example, we state a theorem that provides sufficient conditions for existence and uniqueness of solutions to . Existence and Uniqueness Theorem: Consider the initial value problem , x(0) = x0. Suppose that f (x) and f ′(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (–τ,τ) about t = 0, and the solution is unique.

4). Thus the graph of N(t) is S-shaped or sigmoid for N0 < K/2. 4 Something qualitatively different occurs if the initial condition N0 lies between K/2 and K; now the solutions are decelerating from the start. Hence these solutions are concave down for all t. If the population initially exceeds the carrying capacity (N0 > K), then N(t) decreases toward N = K and is concave up. Finally, if N0 = 0 or N0 = K, then the population stays constant. Critique of the Logistic Model Before leaving this example, we should make a few comments about the biological validity of the logistic equation.

Nevertheless, we should be aware of what can go wrong in pathological cases. 1: Show that the solution to unique. starting from x0 = 0 is not Solution: The point x = 0 is a fixed point, so one obvious solution is x(t) = 0 for all t. The surprising fact is that there is another solution. To find it we separate variables and integrate: so . Imposing the initial condition x(0) = 0 yields C = 0. ■ When uniqueness fails, our geometric approach collapses because the phase point doesn’t know how to move; if a phase point were started at the origin, would it stay there or would it move according to ?

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