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ERROR ANALYSIS STATISTICS AND OTHER
THE IMPORTANCE OF BEING NONLINEAR
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amplitude applied asymptotic attractor autocorrelation function average behavior biological Brownian motion clusters coefficient concepts constant context curve data set degrees of freedom denote depicted describe deterministic differential equation diffusion dimensional discrete discussion dissipative dynamic energy ensemble equations of motion equilibrium error evolution example exponential fact Figure finite fixed point fluctuations Fokker-Planck equation force Fourier transform fractal fractal dimension frequency Gauss distribution given growth ideas initial integral interval Langevin equation Levy distribution limit cycle linear world view log-normal distribution logistic Lorenz Lorenz attractor mathematical measurements mechanism microscopic mode natural philosophy nonlinear systems observed obtain one-dimensional orbit parameter periodic perturbation phase space phenomena physical sciences population predictability probability density properties quantity random walk relation relaxation oscillator result saturation scaling scientists solitons solution stable statistics stochastic stochastic differential equation superposition term theory tion trajectory variable Verhulst Verhulst equation walkers wave zero