Pattern formation of the attraction-repulsion keller-segel system

Ping Liu, Junping Shi, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

139 Citations (Scopus)


In this paper the pattern formation of the attraction-repulsion Keller-Segel (ARKS) system is studied analytically and numerically By the Hopf bifurcation theorem as well as the local and global bifurcation theorem we rigorously establish the existence of time-periodic patterns and steady state patterns for the ARKS model in the full parameter regimes which are identified by a linear stability analysis We also show that when the chemotactic attraction is strong a spiky steady state pattern can develop Explicit time-periodic rippling wave patterns and spiky steady state patterns are obtained numerically by carefully selecting parameter values based on our theoretical results The study in the paper asserts that chemotactic competitive interaction between attraction and repulsion can produce periodic patterns which are impossible for the chemotaxis model with a single chemical (either chemo-attractant or chemo-repellent).
Original languageEnglish
Pages (from-to)2597-2625
Number of pages29
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number10
Publication statusPublished - 1 Dec 2013


  • Attraction-repulsion chemotaxis
  • Hopf bifurcation
  • Steady state bifurcation
  • Time-periodic patterns.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Pattern formation of the attraction-repulsion keller-segel system'. Together they form a unique fingerprint.

Cite this