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Abstract <p> A nonlinear system describing the dynamics of cancer growth is investigated. For allvalues of the system parameters, the existence of an attractor is proved and positively invariantsets containing it are found. The estimates of ultimate bounds are calculated. All equilibriumpoints are found, and conditions for their existence and bifurcation are proved. In the systemparameter space, sets are found where these conditions are satisfied. Examples of constructingintersections of these sets with two-dimensional planes are given. Other characteristics associatedwith the appearance of periodic trajectories and chaotic dynamics are calculated.</p>

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Ultimate Bounds, Equilibrium Points, and Bifurcations in a Three-Dimensional Cancer Model

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • A. P. Krishchenko

摘要

Abstract

A nonlinear system describing the dynamics of cancer growth is investigated. For allvalues of the system parameters, the existence of an attractor is proved and positively invariantsets containing it are found. The estimates of ultimate bounds are calculated. All equilibriumpoints are found, and conditions for their existence and bifurcation are proved. In the systemparameter space, sets are found where these conditions are satisfied. Examples of constructingintersections of these sets with two-dimensional planes are given. Other characteristics associatedwith the appearance of periodic trajectories and chaotic dynamics are calculated.