RESUMEN
Improving battery health and safety motivates the synergy of a powerful duo: physics and machine learning. Through seamless integration of these disciplines, the efficacy of mathematical battery models can be significantly enhanced. This paper delves into the challenges and potentials of managing battery health and safety, highlighting the transformative impact of integrating physics and machine learning to address those challenges. Based on our systematic review in this context, we outline several future directions and perspectives, offering a comprehensive exploration of efficient and reliable approaches. Our analysis emphasizes that the integration of physics and machine learning stands as a disruptive innovation in the development of emerging battery health and safety management technologies.
RESUMEN
The deadly outbreak of the second wave of Covid-19, especially in worst hit lower-middle-income countries like India, and the drastic rise of another growing epidemic of Mucormycosis, call for an efficient mathematical tool to model pandemics, analyse their course of outbreak and help in adopting quicker control strategies to converge to an infection-free equilibrium. This review paper on prominent pandemics reveals that their dispersion is chaotic in nature having long-range memory effects and features which the existing integer-order models fail to capture. This paper thus puts forward the use of fractional-order (FO) chaos theory that has memory capacity and hereditary properties, as a potential tool to model the pandemics with more accuracy and closeness to their real physical dynamics. We investigate eight FO models of Bombay plague, Cancer and Covid-19 pandemics through phase portraits, time series, Lyapunov exponents and bifurcation analysis. FO controllers (FOCs) on the concepts of fuzzy logic, adaptive sliding mode and active backstepping control are designed to stabilise chaos. Also, FOCs based on adaptive sliding mode and active backstepping synchronisation are designed to synchronise a chaotic epidemic with a non-chaotic one, to mitigate the unpredictability due to chaos during transmission. It is found that severity and complexity of the models increase as the memory fades, indicating that FO can be used as a crucial parameter to analyse the progression of a pandemic. To sum it up, this paper will help researchers to have an overview of using fractional calculus in modelling pandemics more precisely and also to approximate, choose, stabilise and synchronise the chaos control parameter that will eliminate the extreme sensitivity and irregularity of the models.
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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.
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This work proposes new fractional-order (FO) models of six chaotic diseases whose fractional dynamics have not been studied so far in literature. Secondly, design and analysis of suitable controllers to control chaos where present, and that of anticontrollers to generate chaos where absent, for these newly proposed FO models of diseases, are put forward. The proposed controllers and anticontrollers address the problem of the health hazards arising from the dysfunctionalities due to the impact of chaos in these biological models. Controllers to supress chaos in four diseases, namely, FO Diabetes Mellitus, FO Human Immunodeficiency Virus (HIV), FO Ebola Virus and FO Dengue models are designed by Back-stepping, Adaptive Feedback and Sliding Mode Control strategies, whereas anticontrollers to introduce chaos in diseases, namely, FO Parkinson's illness and FO Migraine models, are carried out by Linear State Feedback, Single State Sinusoidal Feedback and Sliding Mode Anticontrol strategies. The equilibrium points, eigenvalues and Lyapunov Exponents of the FO disease models are evaluated and indicate the significance of chaos in them and necessitate upon the requirement of controllers and anticontrollers accordingly. The simulation results in terms of bifurcation diagrams, time series plots and phase portraits confirm the successful accomplishment of the control objectives.
RESUMEN
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.