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Traveling-wave Solution to the Schumpeterian Dynamics with Heterogeneous Imitation

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Abstract

The article studies a Schumpeterian dynamics model describing the interaction of two types of agents with a heterogeneous imitation range. Far-sighted agents have an infinite imitation range and the short-sighted ones have a finite imitation range. The evolution of their complementary distributions is described by the system of coupled Burgers-type equations. The traveling-wave solution of this system is presented with the conditions of existence for both unilateral and mutual influence. In both cases the density of short-sighted agents is captured by the soliton-like propagating density of the far-sighted agents and forms the shock wave as an entropy solution to the inviscid Burgers-type equation. Numerical experiments confirm the results.

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Funding

The research was supported by the RSCF 24-11-00329.

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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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Egorov, L.V. Traveling-wave Solution to the Schumpeterian Dynamics with Heterogeneous Imitation. Lobachevskii J Math 45, 177–190 (2024). https://doi.org/10.1134/S199508022401013X

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  • DOI: https://doi.org/10.1134/S199508022401013X

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