Early Diagnosis of Problems Related to the Self-Organization of the Cardiovascular System Based on the Interplay between RR and JT Cardiac Intervals.

The dynamics of the collapse of complexity observable in the performance of the cardiovascular system during the stress test is investigated in this paper. For this purpose, the interplay between the RR and JT cardiac intervals is measured and assessed for each participant. This case study involves a modest sample size of eight individuals with normal and elevated blood pressure. Although it is anticipated that the interaction between the RR and JT intervals is rather complex during the stress test, the existence of interpretable time delays between those cardiac intervals is demonstrated using the time delayed patterns algorithm. The assessment of the cardiovascular mobilization taking place during the stress test is also an integral part of this study. The velocity of adaptation index Ad and the newly formulated modified adaptation index Ar (computed only for the recovery phase) are used to quantify the healthy mobilization of the cardiovascular system for each participant. The time frequency analysis of the difference signal between the RR and JT intervals is used to quantify the collapse of complexity around the load termination point. Finally, a semi-gauge indication tool is constructed to assess the overall goodness of the self-organization of the cardiovascular system during the stress test.

Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < α < 1.

In this paper, we investigate the generalized fractional maps of the orders 0<α<1. Commonly used in publications, fractional and fractional difference maps of the orders 0<α<1 belong to this class of maps. As an example, we numerically solve the equations, which define asymptotically periodic points to draw the bifurcation diagrams for the fractional difference logistic map with α=0.5. For periods more than four (T>4), these bifurcation diagrams are significantly different from the bifurcation diagrams obtained after 105 iterations on individual trajectories. We present examples of transition to chaos on individual trajectories with positive and zero Lyapunov exponents. We derive the algebraic equations, which allow the calculation of bifurcation points of generalized fractional maps. We use these equations to calculate the bifurcation points for the fractional and fractional difference logistic maps with α=0.5. The results of our numerical simulations allow us to make a conjecture that the cascade of bifurcations scenarios of transition to chaos in generalized fractional maps and regular maps are similar, and the value of the generalized fractional Feigenbaum constant δf is the same as the value of the regular Feigenbaum constant δ=4.669….

Image Entropy for the Identification of Chimera States of Spatiotemporal Divergence in Complex Coupled Maps of Matrices.

Complex networks of coupled maps of matrices (NCMM) are investigated in this paper. It is shown that a NCMM can evolve into two different steady states-the quiet state or the state of divergence. It appears that chimera states of spatiotemporal divergence do exist in the regions around the boundary lines separating these two steady states. It is demonstrated that digital image entropy can be used as an effective measure for the visualization of these regions of chimera states in different networks (regular, feed-forward, random, and small-world NCMM).