Species coexistence is one of the central themes in modern ecology. Coexistence is a prerequisite of biological diversity. However, the question arises how biodiversity can be reconciled with the statement of competition theory, which asserts that competing species cannot coexist. To solve this problem natural selection theory is rejected because it contradicts kinetic models of interacting pop...

Cancer is often characterized as a chaotic, poorly regulated growth. Cancer can be viewed as a complex adaptive system. Complex adaptive systems can be described mathematically by nonlinear (chaos) theory including asymmetry, fractal structure and autocorrelation factor (Cramer, 1993). Atypical shape of tumor cells and chaotic structures of blood flow is one from characteristic of cancer proces...

We present a qualitative analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In similar way to existing works on affine systems (and positively invariant rectangles), we consider here nonlinear Lotka-Volterra n-dimensional equation, in rectangles with any kind of tranverse patterns. We give necessary and sufficient conditions for ...

The peroxidase-oxidase (PO) reaction is an important example of how oscillating reactions arise in living organisms. The reaction is important mathematically because exhibits many characteristics of chaos. Of these characteristics, sensitive dependence on initial conditions illustrates how predicting the future state of the PO reaction is next to impossible. For this reason, chaotic behavior in...

Ecolab and Webworld are both models of evolution produced by adding evolution to ecological equations. They differ primarily in the form of the ecological equations. Both models are self-organised to a state where extinctions balance speciations. However, Ecolab shows evidence of this self-organised state being critical, whereas Webworld does not. This paper examines the self-organised states o...