Search and return model for stochastic path integrators.

Area of Science:

• Theoretical Physics
• Stochastic Processes
• Animal Behavior Modeling

Background:

• A prior stochastic model described object search and return dynamics using constant speed and noise-driven angular dynamics.
• The model incorporated 'pursuit' (return to home) and 'escape' (exploration) behaviors driven by symmetric Lévy-stable noise.

Purpose of the Study:

• To investigate the impact of limited knowledge of home position angle on search and return probabilities.
• To generalize the existing model by introducing a constant shift in the interaction rule, simulating home position uncertainty.
• To analyze the deterministic properties and spatial distribution of the modified dissipative dynamics.

Main Methods:

• Extension of a 2D stochastic model with constant speed and noise-driven angular dynamics.
• Inclusion of symmetric Lévy-stable noise to represent environmental and decision-making influences.
• Introduction of a constant shift parameter to model uncertainty in home position.
• Analysis of deterministic properties and stationary spatial distributions for the generalized model.

Main Results:

• Both noise type and noise strength significantly influence the probability of returning to the home.
• An optimal noise level was previously identified for efficient food source finding.
• Non-vanishing shifts in the interaction rule transform the searcher's kinematics into dissipative dynamics.
• The study calculates the stationary spatial distribution around the home for these dissipative dynamics.

Conclusions:

• Noise characteristics are crucial for optimizing search strategies and return probabilities in stochastic models.
• Introducing home position uncertainty (via shifts) leads to dissipative dynamics with predictable spatial distributions.
• The generalized model provides insights into how imperfect environmental information affects foraging behavior.