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Outline
Name: 马德明
Topic: On Multistability in Chaotic Systems
General purpose:To make more and more people know about chaotic Systems Specific purpose:Explaining the multistability of Chaotic Systems Thesis:The multistability of the chaotic system is not only beautiful but also important in the certain field.I.Introduction
A.Method of getting the attention of audience : Using several interesting pictures to draw out the existence of the chaotic system multistability.B.Statement of purpose:
To introduce the beauty and value of the chaos system multistability and lead more and more people to study it.C.Statement of relevance to the audience:
I want to tell us that the multistability of the chaotic system is not only beautiful but also important in the field of cryptography.D.Preview of the body of the presentation：
Chaotic systems、Multistability、Existence Symmetrical beauty、Encryption application II.Body
A.Main point 1:Existence of multistability in chaotic system A dynamical system with four quadratic nonlinearities is found to display a butterfly strange attractor.In a relatively large region of parameter space the system has coexisting point attractors and limit cycles.At some special parameter combinations, there are five coexisting attractors, where a limit cycle coexists with two equilibrium points and two strange attractors in di erent attractor basins.The basin boundaries have a symmetric fractal structure.In addition, the system has other multistable regimes where a pair of point attractors coexist with a single limit cycle or a symmetric pair of limit cycles and where a symmetric pair of limit cycles coexist without any stable equilibria.B.Main point 2:Constructing multistability in chaotic systems Chaotic dynamical systems that are symmetric provide the poibility of multistability as well as an independent amplitude control parameter.The R¨oler system is used as a candidate for demonstrat-ing the symmetry construction since it is an asymmetric system with a single-scroll attractor.Through the design of symmetric R¨oler sys-tems, a symmetric pair of coexisting strange attractors are produced, along with the desired partial or total amplitude control.III.Conclusion A.Restatement of purpose: Multistability poses a threat for engineering systems because the system may unpre-dictably switch into an undesirable state.Even simple chaotic flows can have such multistable states.Systems with a symmetry are especially vulnerable to multistability since any asymmetric attractor is guaranteed to have a twin attractor symmetric with it.However, multistability may have benefits such as allowing one to simulate and study phenomena in the real world where it also occurs.B.Summary of main points: Existence of multistability in chaotic system is Very beautiful symmetry.In order to achieve a certain function,we Construct multistability in chaotic systems.C.Round off: The world is not the lack of beauty, but the lack of the United States to find the eyes.Chaos theory is a very wonderful existence.I hope there will be more and more people to study it.
