Dynamics of a birth-death process based on combinatorial innovation

Area of Science:

• * Complex Systems Science
• * Innovation Studies
• * Mathematical Modeling

Background:

• * Human creativity often involves combinatorial processes, generating novel ideas or technologies from existing components.
• * Understanding the dynamics of idea generation and extinction is crucial for innovation studies.

Purpose of the Study:

• * To develop a mathematical model for human creativity based on combinatorial processes.
• * To analyze the growth dynamics and 'explosive' phases in the emergence of new ideas or items.
• * To provide a framework for understanding human productivity and creativity patterns.

Main Methods:

• * A stochastic birth-death model with non-linear combinatorial terms was employed.
• * The model incorporates two key parameters (P, α) to capture item generation and extinction.
• * Analytical expressions for mean and variance of 'time to explosion' were derived and compared with simulations.

Main Results:

• * The model exhibits a characteristic 'hockey-stick' growth pattern: slow initial growth followed by rapid expansion.
• * Exact mathematical expressions for the model's key dynamic properties were obtained.
• * Simulations validated the theoretical predictions of the model.

Conclusions:

• * The proposed birth-death model effectively captures the combinatorial nature of human creativity and innovation.
• * The 'hockey-stick' behavior is a predictable outcome of this combinatorial growth process.
• * The model offers a quantitative approach to studying human productivity and creativity, with potential applications in various fields.