Nonlinear Dynamical Economics and Chaotic Motion

algorithm assumed assumption bifurcation value calculated catastrophe theory center manifold chaos chaotic dynamics chaotic motion closed orbits coefficients Consider continuous-time dynamical systems continuous-time systems converges correlation dimension curve depends derivative described determined deterministic differential equation discussion dynamic behavior economic dynamics economic examples eigenvalues emergence equilibrium exist Figure fixed point flip bifurcation forced oscillator function Goodwin model graph growth GUCKENHEIMER/HOLMES 1983 higher-dimensional homoclinic orbit Hopf bifurcation horseshoe map implies initial points invariant set investigated iterations Jacobian Kaldor model Liénard equation limit cycles linear dynamical systems logistic equation Lyapunov exponents mathematical matrix negative neighborhood nonlinear dynamical systems one-dimensional maps original parameter phase space phenomena Poincaré map Poincaré-Bendixson theorem possible prediction presented properties Section stable stable manifold stochastic strange attractor structural stability subspaces theorem tion torus transcritical bifurcation two-dimensional unstable variables vector field WALRAS worldview Xt+1 zero