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Iterated Maps or Difference Equations
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absorbing area Accordingly amplitude attraction basins basin of attraction becomes bifurcation boundary conditions catastrophe catastrophe theory chaos chaotic attractor coefficients complex consider constant coordinates Cournot point critical lines cubic curve defined denoted derivative determinant differential equations dimension dimensional direction display dynamical system economics eigenvalues equal to zero equilibrium fact finite fixed point flow fractal fractal dimension frequency function gradient hence income initial conditions integral intersection interval iteration Laplacian left hand side limit cycle linear linearised logistic map loses stability Lyapunov exponent monkey saddle motion negative node nonlinear nonzero obtain origin oscillator pair parameter value period doubling perturbation methods phase space picture plane population positive potential produce quasiperiodic region represents result right hand side saddle points second order simulation sine solution solve spatial spiral square structural stability Substituting Theorem tion trajectories unstable variables vector vertical wave whereas