Emergent non-Hermitian physics in generalized Lotka-Volterra model

Abstract

In this paper, we study the non-Hermitian physics emerging from a predator-prey ecological model described by a generalized Lotka-Volterra equation. In the phase space, this nonlinear equation exhibits both chaotic and localized dynamics, which are separated by a critical point. These distinct dynamics originate from the interplay between the periodicity and non-Hermiticity of the effective Hamiltonian in the linearized equation of motion. Moreover, the dynamics at the critical point, such as algebraic divergence, can be understood as an exceptional point in the context of non-Hermitian physics.

8 pages

References in corpus (10)

• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• Topological phase transition in coupled rock-paper-scissor cycles
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Topology protects chiral edge currents in stochastic systems
• Antipredator behavior in the rock-paper-scissors model
• Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems

Cited by in corpus (1)

• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry