Mathematical aspects of organization and disorganization in biology

Abstract

In the talk I am going to discuss whether and how it is possible to mathematically model order, that is self-organization, and disorder, that is disorganization, in life systems. I refer to the theory of integro-differential equations, the so-called kinetic equations [1]. I am going to show that the blow-ups of solutions, which usually are treated as “bad”, can actually describe some self-organization, that can, in some cases, be “positive”, like healing processes. The results can be applied to processes in biology; like DNA denaturation; medicine; tendon healing process or invasion of cancer and social sciences; e.g. opinion formation. Moreover, I am going to discuss the importance of nonlocal modeling of some biological phenomena including the invasion of cancer on the surrounding tissue, see [2]. I am going to present various nonlocal models [3, 4], and show their applications.