Dynamical analysis,control,boundedness,and prediction for a fractional-order financial risk system

This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

Robust delay-dependent stability of uncertain inertied neural networks with impulsive effects and distributed-delay

The robust stability problem of uncertain inertial neural networks with impulsive effects and distributed-delay is considered in the present paper.The average impulsive interval and differential inequality for delay differential equations are used to obtain the global exponential stability of the inertial neural networks.The robust distributed-delaydependent stability criteria here are proposed in terms of both linear matrix inequalities and algebraic inequalities.Our results can not only be used to obtain the stability of the uncertain inertial neural network with impulsive disturbance,but also be utilized to design the impulsive control for the uncertain inertial neural networks.The novel criteria complement and extend the previous works on uncertain inertial neural network with/without impulsive effects.Typical numerical examples are used to test the validity of the developed stability criteria finally.