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Dynamics and bifurcations by Jack K. Hale

Dynamics and bifurcations Jack K. Hale ebook
Format: djvu
Page: 291
ISBN: 3540971416, 9783540971412
Publisher: Springer

Review “…the text is mathematically rigorous yet devoid of excess formalism…many excellent illustrations and a wealth of worked and unworked examples. It is also possible to obtain a Hopf bifurcation by increasing the rate of oxygen consumption by tumour cells, σp, thus decreasing the slope of the p-nullcline. The distribution of values for 1000 different realizations of the dynamics is shown in Fig. Initially the distribution is unimodal and starts to broaden until the saddle-node bifurcation (Fig. For a Hopf bifurcation, we require ∂f/∂F = γ∂f/∂L−K and Equation 44, implying (γ−δ)∂f/∂L−K>0. We show For an invariant manifold, f is given by Equation 15, which immediately satisfies detJ = 0; TrJ<0 is guaranteed if E is monotonically increasing in F and L. Tools in dynamical systems theory are employed to obtain analytical results, including the existence of a three-dimensional limit cycle (in the biologically feasible region) by constructing a Poincaré map and using bifurcation theory. He is the author of two books, Difference and Differential Equations with Computer Experiments, and Dynamics and Bifurcations, with Jack Hale, published by Springer-Verlag. LINK: Download Dynamics and bifurcations Audiobook. A qualitative change in behavior is what we often talk about in system dynamics as a change in behavior mode, e.g. In class we talked about families of discrete dynamical systems: functions f_k:\mathbb{R}\to\mathbb{R} in which k is a parameter. To understand joint e ffects of target cells dynamics and intracellular delay on viral dynamics in vivo, we carry out two-parameter bifurcation analysis. Publisher: Springer Page Count: 299. Not a bifurcation, because the behavior is exponential growth either way. Language: English Released: 2002. GO Dynamics, Bifurcations and Control Author: Fritz Colonius, Lars Gr?ne. In particular we focused on bifurcations. ɝ�平常的动力系统分岔分析是我最近在查询Floquet理论的应用时找到的，浏览了这篇的introduction部分后，知道这个方面的工作虽然“The dynamics o ,科学网. Here, we show that a mathematical model of the macronutrient flux balances can capture the long-term dynamics of human weight change; all previous models are special cases of this model.