A revisit to the past plague epidemic (India) versus the present COVID-19 pandemic: fractional-order chaotic models and fuzzy logic control.

India is one of the worst hit regions by the second wave of COVID-19 pandemic and 'Black fungus' epidemic. This paper revisits the Bombay Plague epidemic of India and presents six fractional-order models (FOMs) of the epidemic based on observational data. The models reveal chaotic dispersion and interactive coupling between multiple species of rodents. Suitable controllers based on fuzzy logic concept are designed to stabilise chaos to an infection-free equilibrium as well as to synchronise a chaotic trajectory with a regular non-chaotic one so that the unpredictability dies out. An FOM of COVID-19 is also proposed that displays chaotic propagation similar to the plague models. The index of memory and heredity that characterise FOMs are found to be crucial parameters in understanding the progression of the epidemics, capture the behaviour of transmission more accurately and reveal enriched complex dynamics of periodic to chaotic evolution, which otherwise remain unobserved in the integral models. The theoretical analyses successfully validated by numerical simulations signify that the results of the past Plague epidemic can be a pathway to identify infected regions with the closest scenarios for the present second wave of Covid-19, forecast the course of the outbreak, and adopt necessary control measures to eliminate chaotic transmission of the pandemic.

Can fractional-order coexisting attractors undergo a rotational phenomenon?

This paper presents an interesting phenomenon unobserved so far in literature to the best of the authors' knowledge in fractional-order chaotic systems (FOCSs). It is the rotational phenomenon of fractional-order coexisting attractors. Another significant feature of the newly proposed FOCS is that two 2-wing chaotic attractors coexist in its fractional-order dynamics i.e. α<1. But once the system attains integer-order, the two attractors merge and evolve into a single 4-wing attractor. Furthermore, the authors have drawn its comparison with various well-known FOCSs to prove its superior features. In a novel attempt, the authors have utilised the property of simultaneous existence of coexisting attractors in the FOCS to carry out the synchronisation. A fractional-order circuit implementation with minimum components, has been performed using numerous audio signals with variable frequencies and amplitudes, as test signals. The objectives of the paper are finally achieved as the circuit implementation results are in perfect agreement with those of the theoretical analyses.

Dual mode adaptive fractional order PI controller with feedforward controller based on variable parameter model for quadruple tank process.

The Quadruple Tank Process (QTP) is a well-known benchmark of a nonlinear coupled complex MIMO process having both minimum and nonminimum phase characteristics. This paper presents a novel self tuning type Dual Mode Adaptive Fractional Order PI controller along with an Adaptive Feedforward controller for the QTP. The controllers are designed based on a novel Variable Parameter Transfer Function model. The effectiveness of the proposed model and controllers is tested through numerical simulation and experimentation. Results reveal that the proposed controllers work successfully to track the reference signals in all ranges of output. A brief comparison with some of the earlier reported similar works is presented to show that the proposed control scheme has some advantages and better performances than several other similar works.