# The Evolution of Service Ecosystems Based on the Lotka-Volterra Model
## 7 Conclusions and Future Work  
Business diversification and expansion have become crucial development strategies for modern enterprises, leading large companies to transition from single-business models to diversified business strategies and ultimately to business ecosystems. This shift is driven by user demand, service innovation, and dynamic cooperation among services. Understanding the development patterns of service ecosystems is essential for forming more efficient and effective management mechanisms and assisting enterprises in making informed decisions during service transformation. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \(a_{10}\) & \(a_{11}\) & \(a_{12}\) & \(a_{20}\) & \(a_{21}\) & \(a_{22}\) \\ \hline Automotive \& New Energy & & & & & \\ Material & 0.0162 & \(1.0\times 10^{-3}\) & \(-6.8098\times 10^{-5}\) & 0.1092 & \(2.2618\times 10^{-4}\) & \(-8.9\times 10^{-3}\) \\ \hline Personal Goods \& & & & & & \\ Information Technology & 0.0142 & \(-5.2313\times 10^{-4}\) & \(-2.6769\times 10^{-4}\) & \(-0.0812\) & \(7.6734\times 10^{-4}\) & \(4.6\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: An explanation of the computing experiment system’s demand agent node attributes. This paper introduces the Lotka-Volterra model from biology into the field of service ecosystems as theoretical support for exploring competitive and cooperative relationships among services. The binary Lotka-Volterra model is extended to a ternary model, considering the complexity of services in the ecosystem, including the impact of social environmental factors and service dynamics on service evolution. Through framework design, theoretical numerical simulation, computational experiments, and real-world comparative analysis, this research explores the competitive-cooperative relationships among original services and their impact on the evolution of new composite services. The study finds that moderate competition \(\alpha=0.4\)-\(0.6\) maximizes the emergence of composite services and the survival rate of new services is the highest. In addition, Tesla's success \(\alpha=0.53\) is related to the annual growth rate of ecosystem partnerships, while the decline of Google Glass \(\alpha=-0.52\) is related to developer engagement. Furthermore, the diversity of the ecosystem reaches its peak at \(\alpha=0.5\), exceeding \(\alpha>0.7\). Due to the rapid decline in competitive exclusion. In conclusion, moderate competition among original services promotes the development of new composite services, while overly tight cooperation may limit the market survival and development of new services. In the future, we can consider more factors influencing the evolution of the service ecosystem to improve the model's complexity and adaptability. In addition, we can utilize more mathematical models to study the impact of various factors on the evolution of service ecosystems. Current research on individual services, such as service recommendations and service composition, is abundant, but research on the entire service ecosystem is still in its infancy, with a lack of reliable real-world data. Future studies could gather relevant data and indicators from the evolutionary development of specific enterprises or organizations' service ecosystems to support further research. Conceptualization, B.S. and Y.L. ; methodology, T.L. and X.S. ; software, H.Z. and Y.Y. ; validation, H.Z. and B.S. ; formal analysis, Y.L. ; investigation, B.S. ; resources, Y.Y. and H.Z. ; data curation, B.S. ; writing--original draft preparation, H.Z. ; writing--review and editing, X.S. ; visualization, B.S. ; supervision, L.C. ; project administration, Y.L. and X.S. ; funding acquisition, T.L. All authors have read and agreed to the published version of the manuscript. Supported by the Fundamental Research Funds for the Provincial Universities of Zhejiang GK249909299001-017. Not applicable. Data Availability Statement: Data are contained within the article.