Hopf bifurcation in time-delayed Lotka–Volterra competition systems with advection

ABSTRACT

In this paper, we study time-delayed reaction–diffusion systems with advection subject to Lotka–Volterra competition dynamics over one-dimensional domains. These systems model the population dynamics of two groups of competing species, with one dispersing randomly and the other a combination of random and biased dispersal (to avoid competition). We show that time-delay(s) in the interspecific competition mechanism can induce instability of the homogeneous equilibrium to the reaction–advection–diffusion systems, and further promote the appearance of time-oscillating spatially inhomogeneous distributions of the species. Our results indicate that these time-delayed systems (both single and double time-delays) can be used to model the well-observed time-periodic distributions of interacting species in natural fields, compared to the systems without time-delay(s).

KEYWORDS:

• Time-delay
• Hopf bifurcation
• advection
• periodic solution
• Lotka–Volterra competition system

AMS SUBJECT CLASSIFICATIONS:

• 34K08
• 34K18
• 34K20
• 35R10
• 92E20
• 35B10

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The work was supported by the Fundamental Research Funds for the Central Universities [grant number JBK170167].