Bounding the Dynamics of a Chaotic-Cancer Mathematical Model
المؤلفون المشاركون
Coria, Luis N.
Valle, Paul A.
Gamboa, Diana
Plata, Corina
المصدر
Mathematical Problems in Engineering
العدد
المجلد 2018، العدد 2018 (31 ديسمبر/كانون الأول 2018)، ص ص. 1-14، 14ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2018-11-08
دولة النشر
مصر
عدد الصفحات
14
التخصصات الرئيسية
الملخص EN
The complexity of cancer has motivated the development of different approaches to understand the dynamics of this large group of diseases.
One that may allow us to better comprehend the behavior of cancer cells, in both short- and long-term, is mathematical modelling through ordinary differential equations.
Several ODE mathematical models concerning tumor evolution and immune response have been formulated through the years, but only a few may exhibit chaotic attractors and oscillations such as stable limit cycles and periodic orbits; these dynamics are not that common among cancer systems.
In this paper, we apply the Localization of Compact Invariant Sets (LCIS) method and Lyapunov stability theory to investigate the global dynamics and the main factors involved in tumor growth and immune response for a chaotic-cancer system presented by Itik and Banks in 2010.
The LCIS method allows us to compute what we define as the localizing domain, which is formulated by the intersection of all lower and upper bounds of each cells population in the nonnegative octant, R + , 0 3 .
Bounds of this domain are given by inequalities in terms of the system parameters.
Then, we apply Lyapunov stability theory and LaSalle’s invariance principle to establish existence conditions of a global attractor.
The latter implies that given any nonnegative initial condition, all trajectories will go to the largest compact invariant set (a stable equilibrium point, limit cycles, periodic orbits, or a chaotic attractor) located either inside or at the boundaries of the localizing domain.
In order to complement our analysis, numerical simulations are performed throughout the paper to illustrate all mathematical results and to better explain their biological implications.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Valle, Paul A.& Coria, Luis N.& Gamboa, Diana& Plata, Corina. 2018. Bounding the Dynamics of a Chaotic-Cancer Mathematical Model. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-14.
https://search.emarefa.net/detail/BIM-1209819
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Valle, Paul A.…[et al.]. Bounding the Dynamics of a Chaotic-Cancer Mathematical Model. Mathematical Problems in Engineering No. 2018 (2018), pp.1-14.
https://search.emarefa.net/detail/BIM-1209819
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Valle, Paul A.& Coria, Luis N.& Gamboa, Diana& Plata, Corina. Bounding the Dynamics of a Chaotic-Cancer Mathematical Model. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-14.
https://search.emarefa.net/detail/BIM-1209819
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1209819
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
تقوم هذه الخدمة بالتحقق من التشابه أو الانتحال في الأبحاث والمقالات العلمية والأطروحات الجامعية والكتب والأبحاث باللغة العربية، وتحديد درجة التشابه أو أصالة الأعمال البحثية وحماية ملكيتها الفكرية. تعرف اكثر