Lotka-Volterra machine for a general model of complex biological systems

It has been proven that the generalized Lotka-Volterra equations can express arbitrary continuous functions if there are sufficient hidden nodes that are not assigned by observational data. We show that the generalized Lotka-Volterra equations encompass a description of the same structure as do artificial neural networks. Since the equations can be used as a universal modeling framework, we refer the computational models of the equations as Lotka-Volterra machines (LVMs). We develop a software tool (Java applet) to construct LVMs and identified unknown parameters in the LVM using a genetic algorithm. It is demonstrated that the LVM can model the growth of organs in a plant and the software tool can identify the parameters of the LVM although it may have more than 20 unknown parameters, and that the resulting LVM can correctly forecast the dynamics of organs. Specific aspects of the behaviour of huge LVMs are discussed from examples of simulations. We also propose a self-organizing mechanism according to which a sufficient number of nodes, interconnected by diverse weights in a huge LVM, can maintain their order against fluctuations coming from all other nodes.