Topological phase transition in anti-symmetric Lotka-Volterra doublet chain

Abstract

We present the emergence of topological phase transition in the minimal model of two dimensional rock-paper-scissors cycle in the form of a doublet chain. The evolutionary dynamics of the doublet chain is obtained by solving the anti-symmetric Lotka-Volterra equation. We show that the mass decays exponentially towards edges and robust against small perturbation in the rate of change of mass transfer, a signature of a topological phase. For one of the configuration of our doublet chain, the mass is transferred towards both edges and the bulk is gaped. Further, we confirm this phase transition within the framework of topological band theory. For this we calculate the winding number which change from zero to one for trivial and a non-trivial topological phases respectively.

arXiv comment9 pages, 7 figures

References in corpus (27)

• Berry Phase Effects on Electronic Properties
• Topological Photonics
• Analogs of quantum Hall effect edge states in photonic crystals
• Connectivity of Growing Random Networks
• Topological Boundary Modes in Isostatic Lattices
• Bose-Einstein condensation in complex networks
• Topological mechanics of gyroscopic metamaterials
• Elastic higher-order topological insulator with topologically protected corner states
• Topological phonon modes and their role in dynamic instability of microtubules
• Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
• Topological mechanics of origami and kirigami
• Fermi Level Tuning of Epitaxial Sb2Te3 Thin Films on Graphene by Regulating Intrinsic Defects and Substrate Transfer Doping
• Noise and Correlations in a Spatial Population Model with Cyclic Competition
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems
• Zero range model of traffic flow
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Topological multiband photonic superlattices
• Topological phase transition in coupled rock-paper-scissor cycles
• Condensation in stochastic mass transport models: beyond the zero-range process
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions
• Non-Hermitian topology in rock-paper-scissors games
• Mortality makes coexistence vulnerable in evolutionary game of rock-paper-scissors
• Topological protection can arise from thermal fluctuations and interactions
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Emergence of first-order and second-order phase transitions in a cyclic ecosystem exposed to environmental impact