Titlebook: Dynamics and Bifurcations; Jack K. Hale,Hüseyin Koçak Textbook 1991 Springer-Verlag New York, Inc. 1991 Eigenvalue.bifurcation.difference

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书目名称Dynamics and Bifurcations影响因子(影响力)




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书目名称Dynamics and Bifurcations网络公开度




书目名称Dynamics and Bifurcations网络公开度学科排名




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书目名称Dynamics and Bifurcations被引频次学科排名




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书目名称Dynamics and Bifurcations读者反馈学科排名

欲望小妹

Elementary Bifurcationsation depending on variable parameters. We first illustrate certain key ideas by way of specific examples. Then we generalize these observations and analyze local bifurcations of an arbitrary scalar differential equation. Since the Implicit Function Theorem is the main ingredient used in these gener

子女

Scalar Mapsof applications. Despite the power of numerical approximation schemes as “experimental” tools and their case of implementation on the computer, there is always the difficulty of deciding on the accuracy of computations. Even in the case of a scalar differential equation, one can he confronted with r

Cleave

lavish

Bifurcations of Periodic Equations of Poincaré maps, the study of local bifurcations of periodic solutions is equivalent to the study of bifurcations of fixed points of monotone maps given in Section 3.3. Next, we develop selected ideas from the “method of averaging” and show how to compute higher- order derivatives of the Poincaré

Contort

On Tori and Circlesin ., then it gives rise to a differential equation on a torus (the surface of a doughnut). The dynamics of such equations are explored most conveniently in terms of their Poincaré maps, which happen to be maps on a circle. Accordingly, in the spirit of Chapter 3, we include a brief discussion of su

Contort

heart-murmur

Gyrate

Near Equilibriar foregoing discussions that the stability type of an equilibrium point of a linear system is determined by the eigenvalues of its coefficient matrix. Analogous to the results in Section 1.3, we prove several theorems to show that, under certain conditions, the stability type of an equilibrium point

冒烟

In the Presence of a Zero Eigenvaluevector field has one zero and one negative eigenvalue. Our investigation culminates in the observation that the local dynamics and bifurcations of such a planar system are determined from those of an appropriate scalar differential equation. Analysis of the resulting scalar equation can, of course,