The control effects on the convection dynamics in a viscoelastic fluid-saturated porous medium heated from below and cooled from above are studied. A truncated Galerkin expansion was applied to balance equations to obtain a four-dimensional generalized Lorenz system. The dynamical behavior is mainly characterized by the Lyapunov exponents, bifurcation, and isospike diagrams. The results show that within a range of moderate and high Rayleigh numbers, proportional controller gain is found to enhance the stabilization and destabilization effects on the thermal convection. Furthermore, due to the effect of viscoelasticity, the system exhibits remarkable topological structures of regular regions embedded in chaotic domains.
The range of effectiveness of the novel corona virus, known as COVID-19, has been continuously spread worldwide with the severity of associated disease and effective variation in the rate of contact. This paper investigates the COVID-19 virus dynamics among the human population with the prediction of the size of epidemic and spreading time. Corona virus disease was first diagnosed on January 30, 2020 in India. From January 30, 2020 to April 21, 2020, the number of patients was continuously increased. In this scientific work, our main objective is to estimate the effectiveness of various preventive tools adopted for COVID-19. The COVID-19 dynamics is formulated in which the parameters of interactions between people, contact tracing, and average latent time are included. Experimental data are collected from April 15, 2020 to April 21, 2020 in India to investigate this virus dynamics. The Genocchi collocation technique is applied to investigate the proposed fractional mathematical model numerically via Caputo-Fabrizio fractional derivative. The effect of presence of various COVID parameters e.g. quarantine time is also presented in the work. The accuracy and efficiency of the outputs of the present work are demonstrated through the pictorial presentation by comparing it to known statistical data. The real data for COVID-19 in India is compared with the numerical results obtained from the concerned COVID-19 model. From our results, to control the expansion of this virus, various prevention measures must be adapted such as self-quarantine, social distancing, and lockdown procedures.