Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

Abstract

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.

Cryptographic Algorithm Using Newton-Raphson Method and General Bischi-Naimzadah Duopoly System

“…The general Bischi-Naimzada game is a market vying between two companies based on sales constraints with the aim of maximising profits. The general Bischi-Naimzadah duopoly system is mathematically defined as [ 38 ]: where…”

“…This is because this it contains many chaotic regions for different values of the parameters. The proposed system also shows a great positive feature, which is the emergence of a very wide range of chaos and complex dynamics with the parameter in which the system (1) shows very complex chaotic behavior [ 38 ]. Moreover, incorporating the effects of sales constraints into the form has the advantage of increasing the number of parameters in the form and thus expanding the secret key space for the cryptography process.…”

“…Moreover, incorporating the effects of sales constraints into the form has the advantage of increasing the number of parameters in the form and thus expanding the secret key space for the cryptography process. Also, a stable coexistence of multiple chaotic attractions is observed in this case [ 38 ].…”

Research on Sustainable Development of Mining Goaf Management Based on Economic Models

“…The optimal strategy of the inventory model in which the demand rate potentially depends on both the selling price and the inventory level is given, and the results are illustrated by numerical examples. Askar et al [25] proposed a profit-maximizing economic model considering sales constraints, based on the theory of nonlinear dynamical systems. The influence of key system parameters on the stability and complexity of dynamic game is studied.…”