The innovation for entrepreneurial systems and the advocacy to enact policies that institutionalise it had recently flooded the literature. Every system has fundamental principles responsible for their state, progress and change; such is the impact of the Igbo apprenticeship scheme on the entrepreneurial system. This has recently resulted in many scholars calling for government involvement through enacting policies that will make the scheme all-inclusive for sustainable economic growth in developing economies. Amongst the huge body of literature in its advocacy, none has addressed the question of the underlying principles for reproducing the relations in terms of the mathematical phenomena that the system embodies. This work shows that the success of the Ndịgbo apprenticeship hinges on certain defined underlying metaphorical mathematical functional patterns responsible for the strategic informal management behavioural model. The symbolic characteristics derived from the informal discipleship learning mode are activated for commerce, by young males and their hands-on in trading, with persistent cooperation, integrity, communication and collective purposeful attempts to succeed. The evidence of the model described is extracted from the explorative and exploitative trajectories that emerged from their goal-pursuing dedications to satisfy customer needs, with optimal methods for managing resources and building economies of scale, emerge. This is known as Ịgba-ọsọ-ahịa. This work reveals that Ịgba-ọsọ-ahịa embodies attributes of models that have shaped world-class productive systems such as (a) the geometrical Mandelbrot model, (b) Markov Chain variant with a backoff process, (c) stochastic nonlinear models, (d) network spatial model and (e) system computational model. Finally, a simplistic novel stochastic model of the socio-economic processes is developed to solve complex engineering decisions and hyperparameter optimisation problems in this work.
