Application Modified Hurst Exponent algorithm for the discrete-time food chain

In this paper, persistence, fractal dimension, and predictability index a discrete-time food chain characterized by three species is modeled by a system of three nonlinear difference equations have been studied, where to find the time series of chain food by numerical iterations, stability analysis, identify equilibrium, and fixed points of this dynamic system. The values of modified Hurst exponent (H), fractals dimension (D), and predictability index (PIF) for a food chain were calculated. To know the regularity of the chain by phase space, bifurcation diagrams, and the binary (0-1) test for chaos have been analyzed the basic characteristics of the system. Where modern programming languages Version )maple(16.1) and matlab(7.14) ( used. The results of analysis show that the values of modified Hurst exponent is anti-persistent in most cases the food chain, and that some of the values of the parameters internal equilibrium point loses its stability through bifurcation diagrams