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Linked and knotted chimera filaments in oscillatory systems
1Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada T2N 1N4.
Physical Review. E
|August 31, 2016
Summary
Stable knots and links, such as trefoils and Hopf links, are shown to exist in oscillatory systems. This discovery arises from specific coupling ranges, stabilizing vortex lines and leading to complex topological structures.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Topology
Background:
- Stable knotted and linked vortex lines are known in many systems.
- Their existence in oscillatory systems with nonlocal coupling was previously elusive.
Purpose of the Study:
- To investigate the existence of stable knots and links in oscillatory systems.
- To explore the conditions for their formation and the resulting structures.
Main Methods:
- Numerical simulations of simple, complex, and chaotic oscillatory systems.
- Analysis of vortex line dynamics under varying coupling ranges.
Main Results:
- Stable knots and links (trefoils, Hopf links) were found in oscillatory systems with intermediate coupling ranges.
- Effective repulsive forces between vortex lines stabilize knotted structures.
- Vortex lines correspond to scroll wave chimeras, exhibiting synchrony breaking.
Conclusions:
- Stable topological structures like knots and links can emerge in oscillatory systems.
- Intermediate coupling is crucial for stabilizing these structures.
- Complex oscillatory systems exhibit topological superstructures combining knotted filaments and synchronization defects.
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