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Topological Phase Transition in Coupled Rock-Paper-Scissors Cycles
Johannes Knebel1, Philipp M Geiger1, Erwin Frey1
1Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany.
Topological phases are found in the nonlinear antisymmetric Lotka-Volterra equation, exhibiting robust polarization states in rock-paper-scissors cycles. Solitary waves emerge at phase transitions, revealing new insights into topological dynamics.
Area of Science:
- Nonlinear Dynamics
- Topological Physics
- Theoretical Ecology
Background:
- Topological phases are characterized by protected boundary modes.
- The antisymmetric Lotka-Volterra equation (ALVE) models ecological dynamics like rock-paper-scissors cycles.
- Understanding topological phenomena in nonlinear systems is an active research area.
Purpose of the Study:
- To identify and characterize topological phases within the antisymmetric Lotka-Volterra equation.
- To investigate the manifestation of topological properties in a nonlinear dynamical system.
- To analyze the nature of phase transitions and emergent phenomena in topological ALVE.
Main Methods:
- Analysis of the antisymmetric Lotka-Volterra equation.
- Investigation of a one-dimensional chain of ALVE systems.
- Characterization of polarization states and solitary waves.
- Classification of the topological phase transition within the tenfold way framework.
Main Results:
- Topological phases were identified in the ALVE.
- Robust polarization states were observed in one-dimensional chains of ALVE.
- Solitary waves were found to exist at the transition points between polarization states.
- The topological phase transition was classified under symmetry class D.
Conclusions:
- The ALVE hosts topological phases, extending topological concepts to nonlinear systems.
- Robust polarization and solitary wave phenomena are key signatures of these topological phases.
- The findings connect nonlinear ecological models to fundamental concepts in topological physics, specifically 1D topological superconductors.
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