Orbits in a stochastic Goodwin-Lotka-Volterra model

2013/08/15 by Bernardo Costa-Lima, Costa-Lima, Bernardo, Adrien Nguyen Huu +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Medicine · #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #Economic theories and models #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #math.DS

paper · pdf · doi:10.48550/arxiv.1308.3317

openalex publication_date 2013/08/15 · arxiv created 2014/01/31 · arxiv updated 2014/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 the cycling behavior for a stochastic version, where a Brownian noise is introduced via an heterogeneous productivity factor. Sufficient conditions for existence of the system are provided. We prove that the system produces cycles around an equilibrium point in finite time for general volatility levels, using stochastic Lyapunov techniques for recurent domains. Numerical insights are provided.

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