A Mathematical Model of Regional Socio-Economic Development of Palestine

Abstract

In this study, we describe the socio-economic development in Palestine. Mathematical modeling is used as a tool to explain the main factors that e§ect on the development of Palestine economy. We use two mathematical models to perform the study. The Örst model is in three dimension and the second model is an extension to the Örst model and is in four dimensions. The suggested models are constructed from a set of non-linear continuous di§erential equations which introduce the main study variables (population, jobs, energy and occupation) and coe¢ cients (control vector) that is joint between the two models. At each stage, the proposed models are analyzed mathematically by Önding general and numerical Öxed points. The stability is examined by analyzing Jacobian matrix and the eigenvalues. We clarify the type of bifurcation, direction Öeld diagrams, the numerical solution and the behavior of the system during time. In addition, MATLAB program is used to Önd solutions and to demonestrate the results graphically and numerically. On the other hand, Newton method is used to obtain di§erent values for the basic variables in each stage through some values and observations to give an impression for a progress and improvement in the Öeld of regional economic and social development. Moreover, the value of coe¢ cients are computed based on Palestinian Central Bureau of Statistics (PCBS) by using percentage rate method (growth rate for values). Furthermore, the study cover the occupation period by choosing di§erent base and comparison years for each parameter. The results of numerical simulation and analysis verify the system is chaotic with unstable Öxed points.