Stabilization of Chaos in a Cancer Model: The Effect of Oncotripsy

Abstract

There has been much interest in the development of therapies for the prevention and treatment of tumours. Recently, the method of oncotripsy has been proposed to destroy cancer cells by applying the ultrasound harmonic excitations at the resonant frequency of cancer cells. In this study, periodic disturbances whose frequency tuned to the fundamental frequency and the higher harmonics of the cancer cells are applied to a tumour growth model, respectively, and the appearance of periodic behaviors in a three-dimensional chaotic cancer model is investigated as a result of those harmonic excitations. The numerical results show that by choosing the appropriate values of the parameters of periodic disturbances, the chaotic cancer model induces periodic behaviors such as period-one and two limit cycles which may have important implications on cancer treatment. The results also provide a view to understanding the oncotripsy effect within the framework of stabilization of chaos.

Keywords

• Bifurcation
• Cancer model
• Chaos
• Stabilization

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