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醉染图书非线离散系统中的分岔与稳定9787040552287
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1 Local Stability and Bifurcations
1.1 Discrete Systems
1.2 Fixed—Points and Stability
1.3 Stability Switching
1.3.1 Monotonic and Oscillatory Stability
1.3.2 Spiral Stability
1.4 Local Bifurcations
1.4.1 Monotonic Bifurcations
1.4.2 One—Step Oscillatory Bifurcations
1.4.3 Two—Step Oscillatory Bifurcations
1.4.4 Neimark Bifurcations
References
2 LOW-Dimensional Discrete Systems
2.1 One—Dimensional Discrete Systems
2.2 Monotonic and Oscillatory Stability
. Bifurcations
..1 Monotonic Bifurcations
..2 neStep 0scillatory Bifurcations
.. Two.Step Oscillatory Bifurcations
2.4 Sample Bifurcation Analysis
2.4.1 Saddle—Node Appearing Bifurcations
2.4.2 Saddle—Node Switching Bifurcations
2.4 -3 Third.Order Monotonic Sink Pitchfork Bifurcations
2.4.4 Third一0rder Monotonic Source Pitchfork Bifurcations
2.5 TwO—Dimensional Discrete Systems
2.5.1 Stability and Singularity
2.5.2 An Example
References
3 Global Stability of 1.D Discrete Systems
3.1 Discrete System Classifications
3.2 Fixed—Point Global StabilitV
3-3 One Fixed—Point Systems
3-3.1 Monotonic Stability
3-3.2 Oscillatory Stability
3.4 Two.Fixed.Point Systems
3.4.1 Monotonic Two—Fixed.Point Systems
3.4.2 Oscillatory Two—Fixed—Point Systems
3.5 Thtee—Fixed—Point Systems
3.5.1 Monotonic Three—Fixed.Point Systems
3.5.2 Oscillatory Three—Fixed—Point Systems
References
4 Forward and Backward Discrete Systems
4.1 Yin—Yang Theory Of Discrete Systems
4.2 Forward Discrete Systems
4.3 Backward Discrete Systems
Reference
5 Infinite-Fixed-Point Discrete Systems
5.1 Fixed.Point Computations
5.2 Normal Forms of Discrete Systems
5.3 Infnite—Fixed—Point Systems
5.3.1 0ne—Infinite—Fixed.Point Systems
5.3.2 TWInfinite—Fixed.Point Systems
5.3.3 Higher—Order Infinite—Fixed.Point Systems
5.4 Infinite.Fixed—Point—Network Systems
5.4.1 An Infinite—Fixed—Point.Network System
5.4.2 A Spiral Infinite.Fixed.Point System
5.4.3 A Linear Infinite—Fixed.Point System
5.4.4 A Hyperbolic Infinite—Fixed.Point System
References
Tndex
罗朝俊教授系靠前非线动力学及力学知名专家,目前为美国南伊利诺伊大学爱德华分校突出贡献研究型讲席教授。
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