A MULTI-SPECIES CHEMOTAXIS SYSTEM WITH MULTIPLE CHEMICALS AND LOGISTIC GROWTH

Kurt H. İ., Köroğlu T.

ASERC 4th INTERNATIONAL CONGRESS ON HEALTH, ENGINEERING, ARCHITECTURE and MATHEMATICS, Sankt-Peterburg, Russia, 23 - 29 July 2026, vol.1, no.1, pp.127-132, (Full Text)

  • Publication Type: Conference Paper / Full Text
  • Volume: 1
  • City: Sankt-Peterburg
  • Country: Russia
  • Page Numbers: pp.127-132
  • Karadeniz Technical University Affiliated: Yes

Abstract

ABSTRACT

This study considers a multi-species, multi-chemical chemotaxis model with regular sensitivity and general logistic-type interactions, given by

Here, unknown functions  denote the densities of two species, while  represent the concentrations of chemical substances concentrations of chemical substances. The parameters  and  are chemotactic sensitivities (positive for attraction and negative for repulsion). The functions  describe growth and interaction effects, typically of Lotka–Volterra type. The constants  and  represent production rates of the chemicals. 

Chemotaxis refers to the directed movement of cells or organisms in response to chemical gradients. It plays a crucial role in many biological processes, including population dynamics, tumor growth, immune response, and embryonic development. Mathematically, key challenges in chemotaxis systems include the study of local and global existence, boundedness, finite-time blow-up, and asymptotic behavior of solutions such as persistence, stability, coexistence, and extinction. Over the past decades, these topics have been extensively studied, leading to significant advances in understanding the global dynamics of such systems. 

In this paper, we introduce the above system and discuss its mathematical properties. In particular, we aim to present a framework for analyzing global existence, boundedness, and mass persistence of solutions under suitable assumptions on the nonlinear terms.

Key words: Chemotaxis, multi-species, multi-chemical, regular sensitivity, logistic growth.