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.

In a severely competing economic environment, the competing ability of a company must be improved continuously as the reaction to the outer competition pressure. We propose a model developed from Lotka–Volterra competition model with time dependent parameters other than the equilibrium theory...

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...

Using a simple stochastic growth model, this paper demonstrates that the coefficient of variation of aggregate output or GDP does not necessarily go to zero even if the number of sectors or economic agents goes to infinity. This phenomenon known as non-self-averaging implies that even if the...

A large market economy has a huge number of degrees of freedom with weak microlevel coordination. The 'implicit microfoundations' approach assumes this property of micro-level interactions more strongly conditions macro-level outcomes compared to the precise details of individual choice...