Modeling scaled processes and 1/fβnoise using nonlinear stochastic differential equations

摘要: We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of signal intensity, 1/fβ noise, autocorrelations second-order structural (height–height correlation) functions. Analytical expressions for such characteristics are derived a comparison numerical calculations is presented. The reveal links between proposed model models where consist bursts characterized by burst size, duration interburst time, as in case avalanches self-organized critical extreme event return times long-term memory processes. approach presented may be useful modeling long-range scaled processes exhibiting 1/f noise distributions.