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Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 30 Sayı: 1

Persistence and boundedness in a logistics chemotaxis system including one-species, two-chemicals, and singularity

Tek Tür, İki Kimyasal ve Tekillik İçeren Lojistik Bir Kemotaksi Sisteminde Süreklilik ve Sınırlılık

Mustafa Ekici(ÇANAKKALE ONSEKİZ MART ÜNİVERSİTESİ, ÇANAKKALE TEKNİK BİLİMLER MESLEK YÜKSEKOKULU)0000-0003-2494-8229
Pages
191–197
Publication Date
2026-04-24
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These findings advance previous theoretical results by clarifying how logistic regulation stabilizes chemotactic aggregation even under singular sensitivity.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Chemotaxis systems describe how biological populations respond to chemical gradients, yet singular sensitivities often lead to blow-up phenomena that challenge mathematical stability.
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Key Findings & Data:This study addresses a parabolic–elliptic–elliptic chemotaxis model involving one species and two interacting chemicals with a logistic growth term under homogeneous Neumann boundary conditions.
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Conclusion & Impact:These findings advance previous theoretical results by clarifying how logistic regulation stabilizes chemotactic aggregation even under singular sensitivity.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Kemotaksi · çok türlü sistem · tekil duyarlılık

Abstract

Chemotaxis systems describe how biological populations respond to chemical gradients, yet singular sensitivities often lead to blow-up phenomena that challenge mathematical stability. This study addresses a parabolic–elliptic–elliptic chemotaxis model involving one species and two interacting chemicals with a logistic growth term under homogeneous Neumann boundary conditions. Motivated by the need to identify mechanisms preventing blow-up, we establish rigorous conditions ensuring persistence and global boundedness of classical solutions. Specifically, it is proven that when the logistic damping effect is sufficiently strong, the system admits a unique global solution that remains positive and uniformly bounded over time. These findings advance previous theoretical results by clarifying how logistic regulation stabilizes chemotactic aggregation even under singular sensitivity.

Özet

Kemotaksi sistemleri, biyolojik popülasyonların kimyasal gradyanlara tepkisini tanımlar; ancak tekil duyarlılıklar, matematiksel kararlılığı zorlaştıran patlama (blow-up) olgularına yol açabilmektedir. Bu çalışma, tek tür ve iki etkileşen kimyasal madde içeren, lojistik büyüme terimiyle desteklenmiş parabolik–eliptik–eliptik tipte bir kemotaksi modelini homojen Neumann sınır koşulları altında ele almaktadır. Patlamayı önleyen mekanizmaların belirlenmesi gerekliliğinden hareketle, klasik çözümlerin sürekliliği ve küresel sınırlılığı için yeterli koşullar titizlikle ortaya konmuştur. Özellikle, lojistik sönüm etkisi yeterince güçlü olduğunda sistemin zamana bağlı olarak pozitifliğini koruyan benzersiz ve küresel olarak sınırlı bir çözüme sahip olduğu kanıtlanmıştır. Bu bulgular, lojistik düzenlemenin tekil duyarlılığa rağmen kemotaktik birikimi nasıl dengelediğini ortaya koyarak önceki teorik sonuçları geliştirmektedir.

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Cite This Article

Ekici, M. (2026). Persistence and boundedness in a logistics chemotaxis system including one-species, two-chemicals, and singularity. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 30 Sayı: 1, 191–197. https://doi.org/10.19113/sdufenbed.1814925

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