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, Rusya, 23 - 29 Temmuz 2026, cilt.1, sa.1, ss.127-132, (Tam Metin Bildiri)

Yayın Türü: Bildiri / Tam Metin Bildiri
Cilt numarası: 1
Basıldığı Şehir: Sankt-Peterburg
Basıldığı Ülke: Rusya
Sayfa Sayıları: ss.127-132
Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.