# Multiple scroll wave chimera states

## TL;DR

This paper investigates multiheaded scroll wave chimera states in a 3D Kuramoto model, demonstrating how the number of incoherent domains can grow additively through a cloning procedure, revealing stable and unstable chimera configurations.

## Contribution

It introduces a cloning method to generate multiheaded scroll wave chimeras and analyzes their stability, expanding understanding of complex spatiotemporal patterns in 3D oscillator systems.

## Key findings

- Multiheaded chimeras can be generated via cloning and scale transformation.
- Stable multiheaded chimeras include those with spiral structures like Hopf links.
- Non-spiral 3D chimeras tend to be unstable and quickly destroyed.

## Abstract

We refer the appearance of three-dimensional (3D) multiheaded chimera states that display cascades of self-organized spatiotemporal patterns of coexisting coherence and incoherence. We demonstrate that number of the incoherent chimera's domains can grow additively under appropriate varying the system parameters generating thereby head-adding cascades of the scroll wave chimeras. The phenomenon is derived for Kuramoto model of N identical phase oscillators placed in the 3D cube with periodic boundary conditions, parameters are coupling radius $r$ and phase lag $\alpha$. To obtain the multiheaded chimeras, we perform the so-called 'cloning procedure' as follows: choose a sample single-headed 3D chimera state, make appropriate scale transformation, and put some number of copies of them into the unit cube. After, start numerical simulations with slightly perturbed initial conditions for long enough time to confirms or denies the state existence and stability. It is found, by this a way, that multiple scroll wave chimeras including those with incoherent rolls, Hopf links and trefoils admit this sort of multiheaded regeneration. On the other hand, multiple 3D chimeras without spiral rotations, like coherent and incoherent balls, tubes, crosses, and layers appear to be unstable under are destroyed rather fast even with any small perturbations.