RESUMEN
In this paper, we propose a new mathematical model of cardiovascular system coupled with a respiratory system to study the effects of COVID-19 on global blood circulation parameters using the lumped parameters model. We use the fourth-order Runge-Kutta method for solving the sets of equations of motion. We validate our model by showing that the simulated flows in pulmonary and aortic valves corroborate, respectively, the results established by Smith et al. [IFAC Proceedings Volumes, 39 (2006) 453-458]. Then we examine the effects of the new coronavirus (covid-19) on the cardiopulmonary system through the impact of the high respiratory frequency and the variation of the alveoli volume. To achieve this aim, we propose a new exponential law for the time varying of the pulmonary resistance. It appears that when the respiratory frequency grows, the delay between the systemic artery flow and the flow in the pulmonary artery diminishes. Therefore, the efficiency of the cardiac pump is reduced. Moreover, our results also show that variations of the alveoli volume cause the increment of the pleural pressure in the vascular cavities that induces an exponential growth of the pulmonary resistance. Furthermore, this growth of the pulmonary resistance provokes the augmentation of pressure in some organs and its reduction in others. We found that patient with covid-19 having a prior history of cardiovascular diseases is exposed to a severe case of inflammation/damage of certain organs than those with no history of cardiovascular disease.
RESUMEN
In the framework of a project on simple circuits with unexpected high degrees of freedom, we report an autonomous microwave oscillator made of a CLC linear resonator of Colpitts type and a single general purpose operational amplifier (Op-Amp). The resonator is in a parallel coupling with the Op-Amp to build the necessary feedback loop of the oscillator. Unlike the general topology of Op-Amp-based oscillators found in the literature including almost always the presence of a negative resistance to justify the nonlinear oscillatory behavior of such circuits, our zero resistor circuit exhibits chaotic and hyperchaotic signals in GHz frequency domain, as well as many other features of complex dynamic systems, including bistability. This simplest form of Colpitts oscillator is adequate to be used as didactic model for the study of complex systems at undergraduate level. Analog and experimental results are proposed.
RESUMEN
A simplified hyperchaotic canonical Chua's oscillator (referred as SHCCO hereafter) made of only seven terms and one nonlinear function of type hyperbolic sine is analyzed. The system is found to be self-excited, and bifurcation tools associated with the spectrum of Lyapunov exponents reveal the rich dynamical behaviors of the system including hyperchaos, torus, period-doubling route to chaos, and hysteresis when turning the system control parameters. Wide ranges of hyperchaotic dynamics are highlighted in various two-parameter spaces based on two-parameter Lyapunov diagrams. The analysis of the hysteretic window using a basin of attraction as argument reveals that the SHCCO exhibits three coexisting attractors. Laboratory measurements further confirm the performed numerical investigations and henceforth validate the mathematical model. Of most/particular interest, multistability observed in the SHCCO is further controlled based on a linear augmentation scheme. Numerical results show the effectiveness of the control strategy through annihilation of the asymmetric pair of coexisting attractors. For higher values of the coupling strength, only a unique symmetric periodic attractor survives.
RESUMEN
We consider a modified Noguchi electrical transmission line and examine the effects of a linear capacitance C(s) on the wave characteristics while considering the semidiscrete approximation. It appears that wave modulations in the network are governed by a dispersive nonlinear Schrödinger equation whose coefficients are shown to be a function of C(s). We show that the use of this linear capacitance makes the filter more selective. We also show that the width of the unstable regions increases while that of the stable regions decreases with C(s) adding consequently the width of the frequency domain where bright solitons exist. Furthermore, we establish the existence of one more region (compared to the work of Marquié et al. [Marquié et al., Phys. Rev. E 49, 828 (1994)]) in the dispersion curve that allows the motion of envelope solitons of higher frequency in the system. Numerical and experimental investigations done on the model confirm our analytical predictions.