Optimization of a time-discrete nonlinear dynamical system from a problem of ecology. An analytical and numerical approach (Q2714029)

The authors state and study the so-called Technology-Emissions-Means (TEM) model for modeling the economic interaction between several players which intend to minimize their emissions \(E_i\) caused by technologies \(T_i\) using expenditures of money \(M_i\) or financial means. The players are linked by technical cooperatives and the market which expresses itself in the nonlinear time-discrete dynamics of the TEM model. This model is based on a general model by \textit{J.~Scheffran} [Strategic Defence. Disarmament and Stability, Marburg University, Marburg (1989)] and can be written as NEWLINE\[NEWLINE \begin{gathered} \Delta E_i(t) = \sum_{j=1}^nem_{ij}(t)M_j(t), \\ \Delta M_i(t) = -\lambda_iM_i(t) \bigl(M^*_i - M_i(t)\bigr)\bigl(E_i(t) + \varphi\Delta E_i(t)\bigr). \end{gathered} NEWLINE\]NEWLINE The first equation describes the time-dependent behavior of the emissions reduced so far by each player. These levels are influenced by financial investigations which are determined by the second equation. The \(em_{ij}\) parameters determine the effect on the emissions of the \(i\)th cooperatives. The integration into the TEM model of the memory parameter \(\varphi\) and the growth parameter \(\lambda\) guarantees a realistic economic market behavior while the \(M_i^*(t)\), \(t\in\mathbb N\), are upper bounds for the financial investigations.NEWLINENEWLINENEWLINEThe aim of the article is to study numerically several possible scenarios of optimal energy management in the framework of the TEM model. Numerical results are based on a qualitative analysis of the TEM model. The results obtained lead to new insights in the joint-implementation program.