In this chapter, we describe growth and cycles in economics as a struggle between capitalists and workers. We first present the Phillips curve (which statistically relates unemployment with the rate of change of nominal wages) and then the Goodwin model. The latter reinterprets, in economical...

We present an extension of the Goodwin growth-cycle model that considers the rate of capacity utilization as a new variable in an adapted Lotka-Volterra system of differential equations. We derive a differential equation for the capacity utilization that is proportional to the difference between...

Computer simulations of complex food-webs are important tools for deepening our understanding of these systems. Yet most computer models assume, rather than generate, key system-level patterns, or use mathematical modeling approaches that make it difficult to fully account for nonlinear...

We show that any quasi-polynomial invariant of a quasi-polynomial dynamical system can be transformed into a quasi-polynomial invariant of a homogeneous quadratic Lotka–Volterra dynamical system. We show how this quasi-polynomial invariant can be decomposed in a simple manner. This...

In this paper, we deal with a discrete n-species non-autonomous Lotka–Volterra competitive systems with infinite delays and feedback control, obtain sufficient conditions for the permanence of the systems.

The generalized Lotka–Voltera (GLV) formalism has been introduced in order to explain the power law distributions in the individual wealth (wi(t)) (Pareto law) and financial markets returns (fluctuations) (r) as a result of the auto-catalytic (multiplicative random) character of the individual...

This paper analyzes a model for the competition dynamics of web sites in the Internet, based on the Lotka–Volterra competition equations. This model shows the well known appearance of a winner-take-all characteristic and is based in the nonvalidity of traditional offer and demand equilibrium...

A model for ideological struggles is formulated. The underlying set is a closed one, like a country but in which the population size is variable in time. The dynamics of the struggle is described by model equations of Verhulst–Lotka–Volterra kind. Several “ideologies” compete to increase...