Python code generating the data of figures 2, 3, 4, 5 and 6 of the manuscript: The evolution of cooperation in the unidirectional linear division of labour of finite roles

The evolution of cooperation is an unsolved mystery, which we see in many social and biological systems. In the study titled \"The evolution of cooperation in the unidirectional linear division of labour of finite roles\", we investigate under which sanction systems and how the evolution of cooperation happens in the linear division of labour. 
This python code has been used to produce the results of Figures 2, 3, 4, 5, and 6 of the manuscript. This code shows the evolution of cooperation among the population of various different groups which have different roles to play in the linear division of labour, on the basis of numerical analysis of a partial differential equation system, which originates from the replicator equations used in the evolutionary game theory.  We find the locally stable equilibria using this code, which shows the ultimate results of the dynamics in the system under given parameters. Figures 3, 5, and 6 are direct products of the code, showing the dynamics of a system..., These are python codes for numerical simulation of replicator equations to generate figures 2, 3, 4, 5, and 6 of the study titled \"The evolution of cooperation in the unidirectional linear division of labour of finite roles\". For making the code easier to read, .pdf version is given.,