Research Papers: Design Theory and Methodology

Technology Evolution Prediction Using Lotka–Volterra Equations

[+] Author and Article Information
Guanglu Zhang

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: glzhang@tamu.edu

Daniel A. McAdams

Fellow ASME
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: dmcadams@tamu.edu

Venkatesh Shankar

Center for Retailing Studies Mays
Business School,
Texas A&M University,
College Station, TX 77840
e-mail: vshankar@mays.tamu.edu

Milad Mohammadi Darani

Center for Retailing Studies Mays
Business School,
Texas A&M University,
College Station, TX 77840
e-mail: mmohammadi@mays.tamu.edu

1Corresponding author.

Contributed by the Design Theory and Methodology Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 14, 2017; final manuscript received February 12, 2018; published online March 23, 2018. Assoc. Editor: Christopher Mattson.

J. Mech. Des 140(6), 061101 (Mar 23, 2018) (9 pages) Paper No: MD-17-1275; doi: 10.1115/1.4039448 History: Received April 14, 2017; Revised February 12, 2018

During the development planning of a new product, designers and entrepreneurs rely on the prediction of product performance to make business investment and design strategy decisions. Moore's law and the logistic S-curve model help make such predictions but suffer several drawbacks. In this paper, Lotka–Volterra equations are used to describe the interaction between a product (system technology) and the components and elements (component technologies) that are combined to form the product. The equations are simplified by a relationship table and maturation evaluation in a two-step process. The performance data of the system and its components over time are modeled by simplified Lotka–Volterra equations. The methods developed here allow designers, entrepreneurs, and policy makers to predict the performances of a product and its components quantitatively using the simplified Lotka–Volterra equations. The methods also shed light on the extent of performance impact from a specific module (component technology) on a product (system technology), which is valuable for identifying the key features of a product and for making outsourcing decisions. Smartphones are used as an example to demonstrate the two-step simplification process. The Lotka–Volterra model of technology evolution is validated by a case study of passenger airplanes and turbofan aero-engines. The case study shows that the data fitting and predictive performances of Lotka–Volterra equations exceed those of extant models.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Otto, K. N. , and Wood, K. L. , 2001, Product Design: Techniques in Reverse Engineering and New Product Development, Pearson Education, London.
Lee, T. H. , and Nakicenovic, N. , 1988, “Technology Life–Cycles and Business Decisions,” Int. J. Technol. Manage., 3(4), pp. 411–426. https://www.inderscienceonline.com/doi/abs/10.1504/IJTM.1988.025978?journalCode=ijtm
Shane, S. , 2008, Handbook of Technology Innovation and Management, Wiley, Chichester, UK. [PubMed] [PubMed]
Utterback, J. M. , and Abernathy, W. J. , 1975, “A Dynamic Model of Process and Product Innovation,” Omega, 3(6), pp. 639–656. [CrossRef]
Utterback, J. M. , 1996, Mastering the Dynamics of Innovation, Harvard Business Review Press, Boston, MA.
Grübler, A. , 1998, Technology and Global Change, Cambridge University Press, Cambridge, UK. [CrossRef] [PubMed] [PubMed]
Schaller, R. R. , 1997, “Moore's Law: Past, Present and Future,” IEEE Spectrum, 34(6), pp. 52–59. [CrossRef]
Modis, T. , 2014, An S-Shaped Adventure: Predictions—20 Years Later, Growth Dynamics, Lugano, Switzerland.
Magee, C. L. , Basnet, S. , and Funk, J. L. , 2016, “Quantitative Empirical Trends in Technical Performance,” Technol. Forecasting Soc. Change, 104, pp. 237–246. [CrossRef]
Farmer, J. D. , and Lafond, F. , 2016, “How Predictable is Technological Progress?,” Res. Policy, 45(3), pp. 647–665. [CrossRef]
Yassine, A. A. , and Naoum-Sawaya, J. , 2016, “Architecture, Performance, and Investment in Product Development Networks,” ASME J. Mech. Des., 139(1), p. 011101. [CrossRef]
Zhang, G. , McAdams, D. A. , and Shankar, V. , 2017, “Modeling the Evolution of System Technology Performance When Component and System Technology Performances Interact: Commensalism and Amensalism,” Technol. Forecasting Soc. Change, 125, pp. 116–124. [CrossRef]
Morris, S. A. , and Pratt, D. , 2003, “Analysis of the Lotka–Volterra Competition Equations as a Technological Substitution Model,” Technol. Forecasting Soc. Change, 70(2), pp. 103–133. [CrossRef]
Porter, A. L. , Roper, A. T. , and Mason, T. W. , 1991, Forecasting and Management of Technology, Wiley & Sons, New York.
Pistorius, C. W. I. , and Utterback, J. M. , 1997, “Multi-Mode Interaction Among Technologies,” Res. Policy, 26(1), pp. 67–84. [CrossRef]
Odum, E. , and Barrett, G. , 2005, Fundamentals of Ecology, Thomson Brooks/Cole, Belmont, CA.
Pistorius, C. W. I. , 1994, “A Growth Related, Multi-Mode Framework for Interaction Among Technologies,” M.Sc. thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/handle/1721.1/12081
Modis, T. , 1997, “Genetic Re-Engineering of Corporations,” Technol. Forecasting Soc. Change, 56(2), pp. 107–118. [CrossRef]
Marasco, A. , Picucci, A. , and Romano, A. , 2016, “Market Share Dynamics Using Lotka–Volterra Models,” Technol. Forecasting Soc. Change, 105, pp. 49–62. [CrossRef]
Michalakelis, C. , Sphicopoulos, T. , and Varoutas, D. , 2011, “Modeling Competition in the Telecommunications Market Based on Concepts of Population Biology,” IEEE Trans. Syst., Man, Cybern., Part C (Appl. Rev.), 41(2), pp. 200–210. [CrossRef]
Pistorius, C. W. I. , and Utterback, J. M. , 1996, “A Lotka-Volterra Model for Multi-Mode Technological Interaction: Modeling Competition, Symbiosis and Predator Prey Modes,” Technology Management in a Changing World, Fifth International Conference on Management of Technology, Miami, FL, Feb. 27–Mar. 1, pp. 62–71. https://www.researchgate.net/publication/5176207_A_Lotka-Volterra_model_for_multi-mode_technological_interaction_Modeling_competition_symbiosis_and_predator-prey_modes
Pielou, E. C. , 1969, An Introduction to Mathematical Ecology, Wiley-Interscience, New York.
Dormand, J. R. , and Prince, P. J. , 1980, “A Family of Embedded Runge-Kutta Formulae,” J. Comput. Appl. Math., 6(1), pp. 19–26. [CrossRef]
Naim, A. , and Lewis, K. , 2017, “Modeling the Dynamics of Innovation in Engineered Systems,” ASME Paper No. DETC2017-68180.
Biggs, N. , 1993, Algebraic Graph Theory, Cambridge University Press, Cambridge, UK.
Kundu, P. K. , Cohen, I. M. , and Dowling, D. R. , 2012, Fluid Mechanics, Elsevier, Waltham, MA.
Moré, J. , and Sorensen, D. , 1983, “Computing a Trust Region Step,” SIAM J. Sci. Stat. Comput., 4(3), pp. 553–572. [CrossRef]
Sobieszczanski-Sobieski, J. , Morris, A. , and Van Tooren, M. , 2015, Multidisciplinary Design Optimization Supported by Knowledge Based Engineering, Wiley, UK. [CrossRef]
Kabin, B. , 2013, “Apple's iPhone: Designed in California But Manufactured Fast All Around the World (Infographic),” Entrepreneur, Irvine, CA, Article No. 228315. https://www.entrepreneur.com/article/228315
Iatrou, K. , 2014, 100 Years of Commercial Aviation, HERMES Air Transport Club, Montreal, QC, Canada.
Daly, M. , and Gunston, B. , 2008, Jane's Aero-Engines, Jane's Information Group Limited, Surry, UK.
Wilkinson, P. H. , 1970, Aircraft Engines of the World 1970, Paul H. Wilkinson, Washington, DC.
Gipson, L., 2010, “The Double Bubble D8,” National Aeronautics and Space Administration, Washington, DC, accessed Mar. 8, 2018, https://www.nasa.gov/content/the-double-bubble-d8-0
Grignon, P. , and Fadel, G. , 2004, “A GA Based Configuration Design Optimization Method,” ASME J. Mech. Des., 126(1), pp. 6–15. [CrossRef]
Arendt, J. L. , McAdams, D. A. , and Malak, R. J. , 2012, “Uncertain Technology Evolution and Decision Making in Design,” ASME J. Mech. Des., 134(10), p. 100904. [CrossRef]


Grahic Jump Location
Fig. 1

Two-step simplification of Lotka–Volterra equations for smart phone speed to open an app

Grahic Jump Location
Fig. 5

Six steps to apply Lotka–Volterra equations in technology evolution prediction

Grahic Jump Location
Fig. 4

Predicted system technology performance on historical data (1960–1998)

Grahic Jump Location
Fig. 3

Data fitting result for component technology performance (take-off thrust of turbofan aero-engine) [31,32]

Grahic Jump Location
Fig. 2

Data fitting result for system technology performance (Passenger capacity*speed*ranger of passenger airplane) [30]



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In