Resource-Based Competition for Technological Dominance and Coexistence

Traditional frameworks of innovation diffusion, such as epidemic and Lotka–Volterra–Gause models, treat technological substitution primarily as a population-driven or social communication process, frequently overlooking the critical constraints imposed by external factor scarcities. To address this fundamental economic gap, this study performs a qualitative analysis of exploitative competition between two distinct technologies sharing two complementary resources, modeled via a non-linear system of chemostat-type consumer–resource ordinary differential equations. Technologies are represented as homogeneous populations of elemental firms, where individual output is governed by a ratio-dependent, fixed-proportions Leontief production function integrated with a hyperbolic clearing response. Operating within an open industrial system, the model accounts for resource supply rates and firm exit dynamics. We analytically derive the coordinates of both boundary and interior fixed points within the non-negative orthant of the phase space. By investigating the eigenvalues of the associated Jacobian matrix, we establish necessary and sufficient conditions for local asymptotic stability, competitive exclusion, and technological coexistence, demonstrating that efficiency is determined by a break-even resource availability threshold. Our results reveal that structural reconfigurations of the industry supply plane trigger bifurcations between local dominance and multistability. The latter manifests as a path-dependent, Quastlerian selection of initial conditions rather than inherent technological superiority. Finally, we establish the geometric boundaries of the stable assemblage niche, proving that technological diversity is regulated by resource supply rates. By explicitly incorporating resource scarcity into a dynamical predator–prey framework, the proposed model offers a more robust economic and mathematical foundation for innovation diffusion, providing policymakers with structural insights into the resource allocation strategy and the long-term management of industrial diversity.