Differential Equations and Dynamical Systems
Editorial Reviews
Book Description
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.
Book Info
Gives a thorough treatment of linear systems, moving into an examination of the local and global behavior of nonlinear systems and their bifurcations. Contains material on higher-order Melkinov functions and the bifurcation of limit cycles for planar systems of differential equations. Previous edition: c1996. DLC: Differential equations.
Differential Equations and Dynamical Systems,Lawrence Perko,Springer,0387951164,Differentiable Dynamical Systems,Differentiable dynamical syste,Differential Equations - Partial Differential Equations,Differential equations, Nonlin,Differential equations, Nonlinear,General,Mathematical Analysis,Mathematics,Mechanics - General,Science/Mathematics,System Theory,Differential equations,Flow, turbulence, rheology,Fluid mechanics,Integral equations,Mathematics / Mathematical Analysis
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