# Effects of adaptive acceleration response of birds on collective behaviors

## TL;DR

This paper extends a collective behavior model to include adaptive reactions based on local environment, revealing how such adaptivity induces natural fluctuations and resilience in flock dynamics.

## Contribution

It introduces an adaptive reaction mechanism into the Cucker-Smale model, demonstrating its effects on flock behavior and resilience.

## Key findings

- Adaptive reactions induce collective flock responses.
- Fluctuations in orientation and speed are scale-free.
- Flocks remain sensitive to environmental perturbations.

## Abstract

Collective dynamics of many interacting particles have been widely studied because of a wealth of their behavioral patterns quite different from the individual traits. A selective way of birds that reacts to their neighbors is one of the main factors characterizing the collective behaviors. Individual birds can react differently depending on their local environment during the collective decision-making process, and these variable reactions can be a source of complex spatiotemporal flocking dynamics. Here, we extend the deterministic Cucker-Smale model by including the individual's reaction to neighbors' acceleration where the reaction time depends on the local state of polarity. Simulation results show that the adaptive reaction of individuals induces the collective response of the flock. Birds are not frozen in a complete synchronization but remain sensitive to perturbations coming from environments. We confirm that the adaptivity of the reaction also generates natural fluctuations of orientation and speed, both of which are indeed scale-free as experimentally reported. This work may provide essential insight in designing resilient systems of many active agents working in complex, unpredictable environments.