Titlebook: Dynamical Systems with Applications using MATLAB?; Stephen Lynch Textbook 2014Latest edition The Editor(s) (if applicable) and The Author(

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Differential Equations,and uniqueness theorem..On completion of this chapter the reader should be able to.? solve certain first- and second-order differential equations;.? apply the theory to chemical kinetics and electric circuits;.? interpret the solutions in physical terms.? understand the existence and uniqueness theorem and its implications.

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Limit Cycles,e perturbation methods.On completion of this chapter, the reader should be able to.? Prove existence and uniqueness of a limit cycle.? Prove that certain systems have no limit cycles.? Interpret limit cycle behavior in physical terms.? Find approximate solutions for perturbed systems

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Hamiltonian Systems, Lyapunov Functions, and Stability, able to.? prove whether or not a system is Hamiltonian;.? sketch phase portraits of Hamiltonian systems;.? use Lyapunov functions to determine the stability of a critical point;.? distinguish between stability and asymptotic stability.

stress-response

Bifurcation Theory,ity and bistability.? To introduce the theory of normal forms.On completion of this chapter, the reader should be able to.? describe how a phase portrait changes as a parameter changes.? plot bifurcation diagrams.? take transformations to obtain simple normal forms.? interpret the bifurcation diagrams in terms of physical behavior

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Local and Global Bifurcations,Gr?bner bases..On completion of this chapter the reader should be able to.? bifurcate small-amplitude limit cycles from fine foci;.? solve systems of multivariate polynomial equations;.? bifurcate limit cycles from a center;.? investigate limit cycle bifurcation from homoclinic loops, numerically.

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Chaos Control and Synchronization,sional discrete maps.? To introduce two methods of chaos synchronization.On completion of this chapter the reader should be able to.? control chaos in the logistic and Hénon maps;.? plot time series data to illustrate the control;.? synchronize chaotic systems;.? appreciate how chaos control and synchronization are being applied in the real world.

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A Tutorial Introduction to MATLAB,? To provide a concise source of reference for experienced users.On completion of this chapter the reader should be able to.? use MATLAB and the Symbolic Math Toolbox.? produce simple MATLAB programs.? access some MATLAB commands and programs over the World Wide Web

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Linear Discrete Dynamical Systems,theory to modeling the population of a single species..On completion of this chapter, the reader should be able to.? solve first- and second-order homogeneous linear difference equations;.? find eigenvalues and eigenvectors of matrices;.? model a single population with different age classes;.? predi