Modelling the dynamics of two political parties in the presence of switching

Abstract

This paper generalizes the model proposed by Misra, by considering switching between political parties. In the model proposed, the movements of members from political party B to political party C and vice versa, are considered but the net movement is considered by assuming that [Formula: see text] (a constant), which implies that the movement of members is either from party B to party C or from party C to party B. In this paper we remodel these movements through switching functions to capture how individuals switch between parties. The results provide a more comprehensive synopsis of the dynamics between two political parties.

Keywords: Modelling; Political parties; Simulations; Steady states; Switching function.

Fig. 1

Graphs of  ${\mathit{\theta }}_1$  against  b  for different values of  ${\mathit{\alpha }}_1$

Fig. 2

Graphs of ${\displaystyle \frac{d{\mathit{\theta }}_1}{db}}$ against b by varying ${\mathit{\alpha }}_1$, and setting ${\widehat{\mathit{\theta }}}_1=1$ and $m=25$

Fig. 3

Graphs of the switching function with respect to time

Fig. 4

${\mathit{\beta }}_1={\mathit{\beta }}_2={\displaystyle \frac{1}{24}}$

Fig. 5

${\mathit{\beta }}_1\ne {\mathit{\beta }}_2,{\mathit{\beta }}_1={\displaystyle \frac{1}{24}},{\mathit{\beta }}_2={\displaystyle \frac{1}{36}}$

Fig. 6

Time series plot for parties  B  and  C

Fig. 7

Phase plot for the interior equilibrium $E(b^{\ast },c^{\ast })$

Fig. 8

Variation of B with t for different values of ${\mathit{\alpha }}_1$

Fig. 9

Variation of B with t for different values of ${\widehat{\mathit{\theta }}}_1$

Fig. 10

Variation of C with t for different values of ${\mathit{\alpha }}_2$

Fig. 11

Variation of C with t for different values of ${\widehat{\mathit{\theta }}}_2$