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2 International Journal of Applied Mathematics and Computer Science

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Global stability of nonlinear feedback systems with fractional positive linear parts

Kaczorek Tadeusz

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 3

493--499

The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1,−1/k2).

Logistic Equations in Tumour Growth Modelling

Foryś U., Marciniak-Czochra A.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 3

317-325

The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in the paper. The results are illustrated using computer simulations.