Dynamic analysis and adaptive modified projective synchronization for systems with Atangana-Baleanu-Caputo derivative: A financial model with nonconstant demand elasticity

The inherent instability of the financial system itself may lead to chaos and unpredictable economic disorder. It is meaningful to study the stability and control theory of financial chaotic system. Based on the definition of Atangana-Baleanu-Caputo fractional derivative, this work extends the integer-order financial chaotic system with nonconstant demand elasticity to a fractional-order system, and analyzes its nonlinear dynamic properties. The dynamic behavior of the system is discussed by phase diagram, bifurcation diagram, the Largest Lyapunov Exponent (LLE) and 0–1 test method. An adaptive controller is designed to realize the modified projection synchronization of the system. The results can help to improve the understanding of the complex financial system, and provide theoretical support for the formulation of financial intervention strategies.