# Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points

## TL;DR

This paper demonstrates that in certain non-autonomous discrete dynamical systems, a fixed point that is a repeller in autonomous cases can become an attractor in the combined system, illustrating a Parrondo's paradox.

## Contribution

It introduces a novel paradoxical phenomenon where non-hyperbolic fixed points switch from repeller to attractor in periodic non-autonomous systems.

## Key findings

- Repeller fixed points can become attractors in non-autonomous systems
- The phenomenon is demonstrated for non-hyperbolic fixed points
- Provides insight into stability behavior in complex dynamical systems

## Abstract

We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the whole system, giving rise to a Parrondo's dynamic type paradox.