Sensitivity analysis of consumption cycles

Area of Science:

• Economics
• Dynamical Systems
• Stochastic Analysis

Background:

• Economic models often simplify consumer behavior.
• Understanding complex dynamics in consumption is crucial for economic forecasting.
• Stochastic elements introduce realistic unpredictability into economic systems.

Purpose of the Study:

• To investigate the conditions for observing complex attractors in a nonlinear stochastic consumption model.
• To analyze the role of noise intensity and preference adjustment in economic dynamics.
• To apply stochastic sensitivity analysis to a 2-dimensional non-invertible map.

Main Methods:

• Utilizing the stochastic sensitivity function to quantify system response to noise.
• Employing confidence domains to determine the observability of attractors.
• Modeling consumption as a 2-dimensional, non-invertible map with additive stochasticity.

Main Results:

• Established conditions under which a complex consumption attractor becomes observable.
• Demonstrated that noise intensity thresholds for attractor observability are dependent on preference adjustment.
• Quantified the influence of past consumption weighting on the emergence of complex dynamics.

Conclusions:

• The observability of complex consumption attractors is contingent upon noise levels and individual preference structures.
• Stochastic sensitivity analysis provides a robust framework for understanding economic model dynamics.
• Economic behavior exhibits complex, emergent properties influenced by both external randomness and internal adjustment mechanisms.