Bifurcation & stochastic analysis of chaotic finance system through entanglement function

Abstract

Abstract In this novel chaotic financial system, by varying the set-aside bifurcation parameter, the existence of the Hopf bifurcation is investigated. The results are used to discuss equilibrium stability and bifurcations in the modern chaotic system. Added to that, there is an element of chaos in mathematical systems with only one positive Lyapunov exponent. Furthermore, there are conditions in which bifurcation is required to achieve chaotic entanglement. The entanglement functions are designed to form an artificially chaotic system such that two or more stable linear subsystems evolve chaotically, no matter how far apart they are. The Gaussian noise is introduced to normalize or bridge the empirical distribution function of the random variables system and check the convergence. Beyond that, the stochastic model emphasizes the relationships between dissipation, phase space flow, and stability. The maximum dissipation of the system increased as the stochastic financial stability increased.