The property of invariable inherited genetic positions in real trajectories of logistic map
The numerical simulation of computers is an important approach for studying chaotic systems. The basic structure of real trajectories of the logistic map can be observed by using the iterative method with lower positions, which includes the root gene position, the common
gene position and the individual gene position. The invariable inherited genetic position of a real trajectory as the root gene position represents the fundamental characteristic of the trajectory, which will be inherited by each true numerical solution within the real trajectory. In this paper, the two types of real trajectories
of the logistic map are introduced, which include the divergence trajectory and the convergence trajectory. The property of the root gene position of divergence trajectories is presented. The maximum number of the root gene position is proved as the length of the root gene position is equal to 1. Experimental results
show the map of the root gene position when the precision of initial conditions is specified to 1 and 2. As the precision of initial conditions is set to 2, the root gene position in the length of 3 possesses a great percentage, which is close to 50%. The similar situation occurs at the root gene position in the length of 1 when
the precision of initial conditions is specified to 1. It suggests the dense distribution of the root gene position in length. Moreover, the permutation and combination of the common gene positions occur in real trajectories with the same root gene position.
CYBERNETICS AND PHYSICS, Vol. 4, No. 3. 2015, 82-89.