Study on the Growth Driving Model of the Enterprise Innovation Community Based on the Lotka–Volterra Model: A Case Study of the Chinese Automobile Manufacturing Enterprise Community

Abstract

The goal of this paper is to establish a feasible three-species equilibrium model to analyze the symbiotic relationship of an automobile manufacturing community. In order to extend the Lotka–Volterra model to empirical analysis, this paper proposes an enterprise community symbiosis model based on a three-dimensional Lotka–Volterra model, as the classical two-dimensional Lotka–Volterra model has limited application scenarios. This paper takes the innovation assets of three communities of the Chinese automobile manufacturing industry as samples. The industrial community related to automobile manufacturing consists of the automobile manufacturing population, automobile parts population, and enterprise service industry population. The symbiosis system is empirically analyzed from two aspects: the balanced development of the three populations and the competitive evolution of the three populations. The stability of the model is tested by the data from information technology and the intelligent manufacturing community. In the process of dynamic simulation, the symbiotic relationship between automobile manufacturing-related populations shows a significant “skew symbiotic relationship.” This paper reconstructs the “whole population symbiosis” optimization model as skew distribution is difficult to apply to support collaborative development. The symbiosis optimization under the equilibrium state of the three populations shows that the growth of the three automobile manufacturing industry populations has the possibility of equilibrium and reciprocity. The empirical analysis fully demonstrates the feasibility of this research paradigm. The evolution analysis of the symbiotic system shows that cooperative behavior is better than competitive strategy. The research paradigm proposed in this paper can better analyze the symbiosis mechanism of the enterprise community.

A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion

“…Originating in 1925 from the work of renowned scientist Alfred Lotka and independently developed by Vito Volterra in 1926, this model has become a cornerstone in ecological, biological, epidemiological, and economic studies [1][2][3][4]. One notable application of this model in economics is in modeling the interaction between firms within a market [5], while in epidemiology, it finds use in understanding the spread of infectious diseases [6]. The fundamental assumptions of the model posit that the population sizes of the predator and prey species are determined solely by their interactions with each other and their environment.…”

“…where the functions v 0 (τ), w 0 (τ), v L (τ), and w L (τ) are some familiar functions. A few analytical and computational strategies have been developed to deal with the model problem (2) with initial condition (3) accompanied with boundary condition (4) or (5). Let us mention the G ′ /G-expansion approach [16], the finite difference scheme [17], and the compact implicit-explicit RK type techniques [18].…”