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论文题目：Dynamical system and differential equations Project
论文语言：英语论文 English
论文专业：数学
字数：3000
学校国家：加拿大
是否有数据处理要求：是
您的学校：SFU
论文用于：BA assignment 本科课程作业
补充要求和说明：
1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.)
--- Draw level sets of Lyapunov function.
2. Discuss Perron-Frobenius theorem and how it can be used to prove global stability of solutions(Give an example) .
3. Discuss the stability of solutions of non-autonomous system x=f(x,t). X上面有一点.
4. Discuss bifurcation theory,and show how to(theoretically) characterise varies, bifurcation types apriori (saddle-node,pitchfork,hopf,transcritical).Show to charactrise super and sub-critical pitchfork and hopf.(Give an example of each)
1) transcritical.
2)pitchfork(super and sub-critical)
3)Hopf(super and sub-critical)
4)saddle-node
Due 4月15号Use matlab or maple software.
How to starting the project main ideas: looks like story.
写每一个问题都应该按照这个步骤写:
首先介绍一下lyapunov function theory这个是什么? 写一些这个是做什么的,再应用这个一下. 给一个理论(写一些跟这个联系的定理和证明一下它.给一个怎么操作它,怎么找到它的和给一个算法.再给一个关于这个问题的例子应该还要解析, 每个题目需要写证明,而不是直接得结果``` 要比较详细 然后再Use matlab模拟一下你给的那个例子. 还有给文献就够了.``写作老师还有什么自己的想法可以添加. 谢谢!
这个下面这个是老师正对第1题给的讨论问题的思路.
1. what it is ?
2. motivation/ applications.
3. Theory (Give related theorem and proof (some detail))./mechanics(how to find it and compute it algorithmic).
4. Given some example(one will do but given)
(population biology research: used centre manifold theory to prove backward bifurcation).
5. Limitations/applicability
Non- autonomous→poincare’ section.
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