SC/MATH-4271 3.00:Dynamical-Systems

Course Description:

Iterations of maps and differential equations; phase portraits, flows; fixed points, periodic solutions and homoclinic orbits; stability, attraction, repulsion; Poincaré maps, transition to chaos. Applications: logistic maps, interacting populations, reaction kinetics, forced Van der Pol, damped Duffing and Lorenz equations. Prerequisites: SC/MATH 2270 3.00; SC/MATH 1021 3.00 or SC/MATH 2221 3.00 or SC/MATH 1025 3.00.

Language of Instruction:

English

Term W     Section M
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Section Director: Huaiping Zhu
Type
Day Start
Time		 Duration Location
Cat # Instructor Notes/Additional Fees
LECT 01
T 14:30 90
R 14:30 90
G31A01 Huaiping Zhu Should it be safe to do so this course may meet in person in the classroom assigned.

Math4271 Dynamical Systems syllabus and first class Tuesday 2:30pm

by Huaiping Zhu – 

Number of replies: 0

 

Happy new year !Welcome to the class of Math4271, Dynamical systems.

Math4271 Dynamical Systems Winter 2021

1.    Course Information:

  • Instructor:   Huaiping Zhu, Ross Building, N618   Ext: 66095
  • Email:     huaiping@yorku.ca  
  • Grade policy:  
  • Lectures:    T/R 14:30    Zoom ID: 953 4174 3347 PWD:4271
  • Office Hours: Tuesday and Thursday 14:00-14:30, 16:30-17:00, or by appointment
  • Text Book：（major reference)

    J.K. Hale and H. Kocak: Dynamics and Bifurcations, Springer 1991. （2011）
    M. W. Hirsch, S. Smale, and R. Devaney: Differential Equations, Dynamical Systems, and an Introduction to Chaos. 2th Edition. （2012）

2.    Materials to cover

Course objective: To develop skills in analyzing differential equations and dynamical systems using analytical and qualitative techniques widely applicable in science and engineering.

 Main topics to cover:

·       Linear system of differential equations, solving linear systems

·       Classification of equilibrium for planar systems

·       Local stability analysis and phase plane

·       General properties of Differential Equations, Existence, uniqueness

·       Nonlinear systems and local stability

·       Bifurcations and bifurcation diagram

·       Lower co-dimension bifurcations:

              Saddle-node bifurcation, pitch-fork bifurcations, Hopf bifurcations, homoclinic bifurcation

·       Normal forms for planar systems

·       Poincare maps and applications

·       Oscillations in nonlinear systems

·       Applications in ecology and epidemiology

·       Discrete systems and chaos

3.    References:

 ·        Lawrence, Perko. Differential Equations and Dynamical Systems. Springer, 2011.

·        D.W. Jordan, P. Smith, Nonlinear ordinary differential equations, Oxford University Press 1977.

·        J. Liu: A First Course in the Qualitative Theory of Differential Equations, Prentice Hall, 2003.

·        Y. Kuznetsov. Elements of Applied Bifurcation Theory. Springer NY, 1998 (2nd Edition)

Course Material

https://data.mendeley.com/datasets/xh7gr7wtcj/draft?a=75ddadac-c6fd-4a30-aa1d-90b18da088df