Dynamical Systems With Applications Using Maple
This introduction to the theory of dynamical systems utilizes MAPLE to facilitate the understanding of the theory and to deal with the examples, diagrams, and exercises. A wide range of topics in differential equations and discrete dynamical systems is discussed with examples drawn from many different areas of application, including mechanical systems and materials science, electronic circuits and nonlinear optics, chemical reactions and meteorology, and population modeling.
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Linear Systems in the Plane 35
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age class algorithm applied bifurcation diagram bistable region box-counting chaotic attractor Consider constructed critical point defined determine differential equations display dynamical systems eigenvalues eigenvalues and eigenvectors eigenvectors example fixed point flow fractal dimension given in Figure graph Hamiltonian systems harvesting Hence Henon map homoclinic hyperbolic infinite number initial conditions invariant Jacobian Julia sets Koch curve Lienard systems limit cycle logistic map Lyapunov exponent Lyapunov function Maple Commands Maple package mathematical matrix multifractal nonlinear optical orbit origin is unstable oscillations periodic behavior phase plane phase portrait Phys plotted in Figure Poincar6 map points at infinity points of period polynomial population predator-prey predators prove quadrant reader saddle point Section shown in Figure simple small-amplitude limit cycles solution curves solving species stable limit cycle stage Theorem theory three critical points three-dimensional two-dimensional unstable focus unstable manifold unstable node vector field with(plots zero