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1-010-AtmosphericCO2Bifurcation-TechniqueNarrative

Author(s): Jakob Kotas

Keywords: carbon dioxide Surface Atmosphere Exchange bifurcation fold bifurcation saddle node

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Abstract

Resource Image Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

For low values of carbon dioxide there are three equilibrium points: one stable corresponding to present day temperatures, one stable corresponding to much higher temperatures, and an unstable in between. Once carbon dioxide is raised above the bifurcation point, the low-stable and unstable equilibrium point annihilate one another (a saddle-node bifurcation), resulting in the system converging to the lone remaining high-stable equilibrium point.

Students will use both graphing and numerical techniques to find equilibrium points. Matlab software for numerical solution of the ODE is included in an attached file.

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Author(s): Jakob Kotas

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