本书从数学的角度初步介绍了定性微分方程和离散动力系统，包括了理论性证明、计算方法和应用。全书分两部分，即微分方程的连续时间和动力系统的离散时间，可分别用于一学期的课程， 或两者结合为一年期的课程。
Preface
Historical Prologue
Part 1． Systems of Nonlinear Differential Equations
Chapter 1． Geometric Approach to Differential Equations
Chapter 2． Linear Systems
2．1． Fundamental Set of Solutions
Exercises 2．1
2．2． Constant Coefficients： Solutions and Phase Portraits
Exercises 2．2
2．3． Nonhomogeneous Systems： Time-dependent Forcing
Exercises 2．3
2．4． Applications
Exercises 2．4
2．5． Theory and Proofs
Chapter 3． The Flow： Solutions of Nonlinear Equations
3．1． Solutions of Nonlinear Equations
Exercises 3．1
3．2． Numerical Solutions of Differential Equations
Exercises 3．2
3．3． Theory and Proofs
Chapter 4． Phase Portraits with Emphasis on Fixed Points
4．1． Limit Sets
Exercises 4．1
4．2． Stability of Fixed Points
Exercises 4．2
4．3． Scalar Equations
Exercises 4．3
4．4． Two Dimensions and Nullclines
Exercises 4．4
4．5． Linearized Stability of Fixed Points
Exercises 4．5
4．6． Competitive Populations
Exercises 4．6
4．7． Applications
Exercises 4．7
4．8． Theory and Proofs
Chapter 5． Phase Portraits Using Scalar Functions
5．1． Predator-Prey Systems
Exercises 5．1
5．2． Undamped Forces
Exercises 5．2
5．3． Lyapunov Functions for Damped Systems
Exercises 5．3
5．4． Bounding Functions
Exercises 5．4
5．5． Gradient Systems
Exercises 5．5
5．6． Applications
Exercises 5．6
5．7． Theory and Proofs
Chapter 6． Periodic Orbits
6．1． Introduction to Periodic Orbits
Exercises 6．1
6．2． Poincare-Bendixson Theorem
Exercises 6．2
6．3． Self-Excited Oscillator
Exercises 6．3
6．4． Andronov-HopfBifurcation
Exercises 6．4
6．5． Homoclinic Bifurcation
……
Part 2． Iteration of Functions
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