TY - GEN

T1 - A contextual quantum-based formalism for population dynamics

AU - Aerts, Diederik

AU - Czachor, Marek

AU - Sozzo, Sandro

PY - 2010/1/1

Y1 - 2010/1/1

N2 - Population ecology is mainly based on nonlinear equations of the Lotka-Volterra type, which provide mathematical models for describing the dynamics of interacting species. However, for many interacting populations, these equations entail complex dynamical behavior and unpredictability, generating such difficulties and problematical situations as illustrated by the "paradox of the plankton" and the "paradox of enrichment", for instance. A careful analysis shows that an ecosystem is a fundamentally contextual system, hence any formalism describing such systems should incorporate contextuality from the very beginning. But existing approaches are based on classical physics and probability theory, and introduce contextuality as an external effect, so that they cannot generally explain the main peculiarities of ecosystems. Basing ourselves on a contextual formalism elaborated to study microscopic systems in quantum mechanics and including appropriate non-linear equations, we construct a generalization of the Lotka-Volterra equations for contextual systems, apply these equations to discuss some paradoxical situations encountered in ecology, and propound alternative solutions to those currently existing in the literature.

AB - Population ecology is mainly based on nonlinear equations of the Lotka-Volterra type, which provide mathematical models for describing the dynamics of interacting species. However, for many interacting populations, these equations entail complex dynamical behavior and unpredictability, generating such difficulties and problematical situations as illustrated by the "paradox of the plankton" and the "paradox of enrichment", for instance. A careful analysis shows that an ecosystem is a fundamentally contextual system, hence any formalism describing such systems should incorporate contextuality from the very beginning. But existing approaches are based on classical physics and probability theory, and introduce contextuality as an external effect, so that they cannot generally explain the main peculiarities of ecosystems. Basing ourselves on a contextual formalism elaborated to study microscopic systems in quantum mechanics and including appropriate non-linear equations, we construct a generalization of the Lotka-Volterra equations for contextual systems, apply these equations to discuss some paradoxical situations encountered in ecology, and propound alternative solutions to those currently existing in the literature.

KW - Contextuality

KW - Population dynamics

KW - Quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=79960115211&partnerID=8YFLogxK

M3 - Conference paper

AN - SCOPUS:79960115211

SN - 9781577354901

T3 - AAAI Fall Symposium - Technical Report

SP - 22

EP - 25

BT - Quantum Informatics for Cognitive, Social, and Semantic Processes - Papers from the AAAI Fall Symposium, Technical Report

PB - AI Access Foundation

T2 - 2010 AAAI Fall Symposium

Y2 - 11 November 2010 through 13 November 2010

ER -