Dynamics of closed ecosystems described by operators

Abstract

We adopt the so-called occupation number representation, originally used in quantum mechanics and recently adopted in the description of several classical systems, in the analysis of the dynamics of some models of closed ecosystems. In particular, we discuss two linear models, for which the solution can be found analytically, and a nonlinear system, for which we produce numerical results. We also discuss how a damping effect could be effectively implemented in the model.

A phenomenological operator description of dynamics of crowds: Escape strategies

“…We only mention here that this kind of approach has revealed successful not only to describe the migration of a population, as previously said, but also the dynamics of several other macroscopic models, such as stock markets, love affairs or closed ecosystems (see Ref. [20,21,22]).…”

“…The first strategy refers to what has been recently proposed in Ref. [21], i.e., an effective mechanism to describe damping. In fact, it has been shown that, adding a small negative imaginary part to a single parameter of the free hamiltonian produces such a damping.…”

One-directional quantum mechanical dynamics and an application to decision making

“…Playing with the parameters, we were able to produce an equilibrium for the system far from desertification. A similar idea was also used in the description of closed ecosystems, [25], to model systems whose efficiency in recycling garbage into nutrients is not perfect. It is clear that, in this way, we are giving up the hypothesis that the full Hamiltonian of the system should be self-adjoint.…”

Modeling interactions between political parties and electors

“…Among all the strategies adopted during the years to build up models of some specific phenomenon, in recent years many researchers started to use methods typically connected with quantum mechanics, even when dealing with macroscopic systems. This has been done in decision-making processes, [22,21,12,1,2,3], in population dynamics, [6,20], in ecological processes, [4,9,15], and, recently, in the analysis of political systems, [23,24,5,7,8]. In these latter papers, the general operatorial settings analyzed in details in [3] have been used in the description of a political system consisting of three parties interacting among them and with a basin of electors and of undecided voters.…”