Orbits in a stochastic Goodwin–Lotka–Volterra model |
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Authors: | A Nguyen Huu B Costa-Lima |
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Institution: | 1. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil;2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada |
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Abstract: | This paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the Lotka–Volterra model, the Goodwin model. We provide a characterization of orbits in the deterministic highly non-linear model. We then study a stochastic version, with Brownian noise introduced via a heterogeneous productivity factor. Existence conditions for a solution to the system are provided. We prove that the system produces cycles around a unique equilibrium point in finite time for general volatility levels, using stochastic Lyapunov techniques for recurrent domains. Numerical insights are provided. |
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Keywords: | Lotka&ndash Volterra model Goodwin model Brownian motion Random perturbation Business cycles Stochastic Lyapunov techniques |
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