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In this paper, we analyse Turing instability and bifurcations in a host–parasitoid model with nonlocal effect. For a ordinary differential equation model, we provide some preliminary analysis on Hopf bifurcation. For a reaction–diffusion model with local intraspecific prey competition, we first explore the Turing instability of spatially homogeneous steady states. Next, we show that the model can undergo Hopf bifurcation and Turing–Hopf bifurcation, and find that a pair of spatially nonhomogeneous periodic solutions is stable for a(8,0)-mode Turing–Hopf bifurcationand unstable for a(3,0)-mode Turing–Hopf bifurcation. For a reaction–diffusion model with nonlocal intraspecific prey competition, we study the existence of the Hopf bifurcation, double-Hopf bifurcation, Turing bifurcation, and Turing–Hopf bifurcation successively, and find that a spatially nonhomogeneous quasi-periodic solution is unstable for a(0,1)-mode double-Hopf bifurcation. Our results indicate that the model exhibits complex pattern formations, including transient states, monostability, bistability, and tristability. Finally, numerical simulations are provided to illustrate complex dynamics and verify our theoretical results.
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Instability and momentum bifurcation of a molecular Bose-Einstein condensate in a shaken lattice with exotic dispersion
We place a molecular Bose-Einstein condensate in a 1D shaken lattice with a Floquet-engineered dispersion, and observe the dynamics in both position and momentum space. At the initial condition of zero momentum, our engineered dispersion is inverted, and therefore unstable. We observe that the condensate is destabilized by the lattice shaking as expected, but rather than decaying incoherently or producing jets, as in other unstable condensates, under our conditions the condensate bifurcates into two portions in momentum space, with each portion subsequently following semi-classical trajectories that suffer minimal spreading in momentum space as they evolve. We can model the evolution with a Gross-Pitaevskii equation, which suggests the initial bifurcation is facilitate by a nearly linear “inverted V”-shaped dispersion at the zone center, while the lack of spreading in momentum space is facilitated by interactions, as in a soliton. We propose that this relatively clean bifurcation in momentum space has applications for counter-diabatic preparation of exotic ground states in many-body quantum simulation schemes.
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- Award ID(s):
- 1941985
- PAR ID:
- 10494242
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review A
- Volume:
- 108
- Issue:
- 5
- ISSN:
- 2469-9926
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevA.108.L051302
