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Some remarks on the compatibility between determinism and unpredictability
1Université de Lyon, ENS de Lyon &, IXXI, Rhône-Alpine Institute of Complex Systems, Lyon, France. Sara.Franceschelli@ens-lyon.fr
Progress in Biophysics and Molecular Biology
|May 24, 2012
Summary
Deterministic systems can exhibit unpredictable behavior. A new "scenario to chaos transition" concept offers predictability for systems sensitive to initial conditions by analyzing control parameter variations.
Area of Science:
- Dynamical Systems Theory
- Chaos Theory
- Developmental Biology
Background:
- Deterministic systems can exhibit unpredictable behaviors when sensitive to initial conditions.
- Understanding this sensitivity is crucial for predicting system dynamics.
- Existing frameworks may not fully capture developmental noise in complex systems.
Purpose of the Study:
- Introduce the concept of "scenario to chaos transition" for predictability in sensitive systems.
- Explore the genesis of this notion using dynamical systems and structural stability.
- Propose a link between dynamical systems and the epigenetic landscape to model developmental noise.
Main Methods:
- Dynamical systems approach to analyze system behavior.
- Considerations of structural stability to understand system robustness.
- Conceptual framework linking dynamical systems to epigenetic landscapes.
Main Results:
- Deterministic flows can lead to unpredictable outcomes due to sensitivity to initial conditions.
- The scenario to chaos transition provides a novel predictability measure for such systems.
- A dynamical systems perspective on the epigenetic landscape offers a framework for developmental noise.
Conclusions:
- Determinism and unpredictability are reconcilable through sensitive initial conditions.
- The scenario to chaos transition enhances predictability in complex systems.
- The epigenetic landscape, viewed through dynamical systems, aids in understanding developmental noise.
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