System evolution prediction and manipulation using a Lotka–Volterra ecosystem model
Section snippets
Background and related work
The descriptive models do not take the interaction between a system and its components into account as stated earlier. To overcome this shortcoming, we seek inspiration in ecology. This section provides the interaction modes between two species in community ecology and their analogies in engineered systems. We also provide background on the Lotka–Volterra equations and extend the equations as a Lotka–Volterra ecosystem model in system evolution prediction.
Mathematical analysis of the Lotka–Volterra ecosystem model and implications for designers
This section presents the functional equivalence and equilibrium point analysis of the Lotka–Volterra ecosystem model. These analyses demonstrate that the Lotka–Volterra ecosystem model can be used as an advanced model in system evolution prediction. The analysis also provides important implications for designers.
Numerical methods for solving the Lotka–Volterra equations
Solving the differential equations given by Eqs. (4), (5), (6), (7) is necessary to apply the Lotka–Volterra ecosystem model in system evolution prediction. Unfortunately, the analytic solution of the Lotka–Volterra equations is not available for the general case. Thus, numerical methods must be implemented to solve the equations. Employing an appropriate numerical method is crucial to apply the Lotka–Volterra equations in system evolution prediction, since numerical instability previously
Application of the Lotka–Volterra ecosystem model for system evolution prediction
The previous sections demonstrate the Lotka–Volterra ecosystem model as an advanced model in system evolution prediction. The ecosystem model covers a variety of mathematical functions and thus has improved data fitting accuracy. The Lotka–Volterra ecosystem model also considers the interaction between the system and its components through the interaction C terms in the ecosystem model. Moreover, we associate the parameters a, b, C in the Lotka–Volterra ecosystem model with their respective
Case study: passenger airplane fuel efficiency
We develop three steps to apply the Lotka–Volterra ecosystem model in Section 4. In this section, we use passenger airplane fuel efficiency as a case study to illustrate each step, which can be applied in similar fashion to other application scenarios. The system (passenger airplane fuel efficiency) interacts with three components (aerodynamics, weight reduction, and aero-engine fuel efficiency) in this case study. The results of this specific case study demonstrate that the system and the
Conclusions and future work
We extend the Lotka–Volterra equations from community ecology to an ecosystem model to predict the system and its components performances. The ecosystem model comprises a set of differential equations that consider symbiosis, commensalism, or amensalism relationship between the component and the system. We demonstrate the ecosystem model as an advanced model in system evolution prediction through functional equivalence and equilibrium point analysis. To apply the ecosystem model in practical
Funding
This material is based in part upon work supported by the National Science Foundation under Award Number CMMI-1550002. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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