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Investigation of the Schumpeterian Dynamics with Heterogeneous Imitation Range

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Abstract

In this paper we study the catch-up development with poor diffusion of new technologies. We present a modification of the Schumpeterian dynamics model that describes the interaction of two types of agents with heterogeneous imitation range. Far-sighted agents have an infinite imitation range and the short-sighted ones have an infinitesimal imitation range. The evolution of their distributions is described by the system of coupled Burgers-type equations. The numerical scheme for this system is constructed using adaptive artificial viscosity method for a nonlinear advection equation. The unilateral influence of far-sighted agents on the short-sighted ones is considered in numerical experiments using the well-known asymptotic behavior of their dynamics without interactions between types.

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Funding

The research was supported by the RSF (grant no. 23-11-00129).

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Authors and Affiliations

  1. Federal Research Center ‘‘Computer Science and Control’’ of the Russian Academy of Sciences, 119333, Moscow, Russia

    L. V. Egorov

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  1. L. V. Egorov
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Correspondence to L. V. Egorov.

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(Submitted by A. A. Shananin)

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Egorov, L.V. Investigation of the Schumpeterian Dynamics with Heterogeneous Imitation Range. Lobachevskii J Math 44, 282–295 (2023). https://doi.org/10.1134/S1995080223010109

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  • DOI: https://doi.org/10.1134/S1995080223010109

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