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Interacting branching process as a simple model of innovation
Vishal Sood1, Myléne Mathieu, Amer Shreim
1University of Calgary, Canada.
Physical Review Letters
|January 15, 2011
Summary
Innovation growth follows a generalized branching process where new inventions pair with existing ones. Unlike mean-field models, this process ensures a finite chance of survival for all innovation rates, avoiding phase transitions.
Area of Science:
- Complex Systems
- Innovation Dynamics
- Mathematical Modeling
Background:
- Understanding the dynamics of innovation is crucial for economic and technological progress.
- Previous models often relied on mean-field approximations, potentially oversimplifying complex interactions.
Purpose of the Study:
- To model innovation as a generalized branching process.
- To investigate the survival probability and growth patterns of innovations.
- To analyze the asymptotic behavior of the model as parameters approach zero.
Main Methods:
- A generalized branching process model was developed.
- Inventions were modeled as entities that reproduce and die with specific probabilities.
- Mathematical analysis was used to determine survival probabilities and growth trajectories.
Main Results:
- No phase transition occurs; survival is possible for all positive innovation rates (p > 0).
- For infinite decay rates (τ = ∞), a bottleneck precedes superexponential growth, aligning with accelerating returns.
- This accelerating growth pattern persists even with finite decay rates.
Conclusions:
- The generalized branching process provides a more robust framework for understanding innovation dynamics.
- The model predicts sustained, accelerating growth in innovation, challenging mean-field predictions of phase transitions.
- The finite survival probability offers a more realistic outlook on the long-term viability of new inventions.
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