Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to no
ise of multiplicative nature. The special properties of multiplicative noise as opposed to additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. We study the various implications of this observation and its applications in various contexts.
The stabilizing effects of local enrichment are revisited. Diffusively coupled host-parasitoid and predator-prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A linear toy mode
l that yields many of the basic qualitative features of this system is presented. The further nonlinear complications are analyzed in the framework of the marginally stable Lotka-Volterra model, and the continuous time analog of the unstable, host-parasitoid Nicholson-Bailey model. The dependence of the results on the migration rate and level of spatial variations is examined, and the possibility of nonlocal effect of enrichment, where local enrichment induces stable oscillations at a distance, is studied. A simple method for basic estimation of the relative importance of this effect in experimental systems is presented and exemplified.
In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of behaviors wid
ely observed in an enormous number of real-life systems in Economics, Sociology, Biology, Ecology and more.
P.W. Anderson proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented system
atically and confirmed repeatedly by successful confrontation with reality. In the social sciences however, the possibilities to stage experiments to validate it are limited. During the 90s a series of dramatic political and economic events have provided the opportunity to do so. We exploit the resulting empirical evidence to validate a simple agent based alternative to the classical logistic dynamics. The post-liberalization empirical data from Poland confirm the theoretical prediction that the dynamics is dominated by singular rare events which insure the resilience and adaptability of the system. We have shown that growth is led by few singular growth centers (Figure 1), that initially developed at a tremendous rate (Figure3), followed by a diffusion process to the rest of the country and leading to a positive growth rate uniform across the counties. In addition to the interdisciplinary unifying potential of our generic formal approach, the present work reveals the strong causal ties between the softer social conditions and their hard economic consequences.
