Nonlinear model of the firefly flash
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ORIGINAL PAPER
Nonlinear model of the firefly flash Debashis Saikia · Madhurjya P. Bora
Received: 9 March 2020 / Accepted: 18 July 2020 © Springer Nature B.V. 2020
Abstract A low dimensional nonlinear model based on the basic lighting mechanism of a firefly is proposed (Saikia and Bora in Nonlinear model of the firefly flash. http://export.arxiv.org/pdf/2002.01183). The basic assumption is that the firefly lighting cycle can be thought to be a nonlinear oscillator with a robust periodic cycle. We base our hypothesis on the wellknown light producing reactions involving enzymes, common to many insect species, including the fireflies. We compare our numerical findings with the available experimental results which correctly predicts the reaction rates of the underlying chemical reactions. Toward the end, a time-delay effect is introduced for possible explanation of appearance of multiple-peak light pulses, especially when the ambient temperature becomes low. Keywords Firefly · Dynamical model · Hopf bifurcation · Time delay · Period doubling bifurcation 1 Introduction Fireflies are fascinating insects which arouse interests in both scientists as well as in poets! It has a basic lighting mechanism which is highly efficient in producing a very cold light [11] without wasting any energy as D. Saikia · M. P. Bora (B) Physics Department, Gauhati University, Guwahati 781014, India e-mail: [email protected]
heat, reaching an efficiency which no man-made artificial light source has achieved so far [4]. Naturally, bioluminescence is a highly intriguing subject and a great deal of research has been devoted to unravel the mystery of this lighting mechanism, which have also resulted in various possible applications [9,16,19,25,30,36,51]. Historically, systematic research on bioluminescence can be traced back to as early as 1930s by Buck and Buck [10], in which they have analysed the phenomena of large scale synchronisation of firefly flashings. Airth and Foerster [2] proposed a bioluminescence model for fungi in 1962. Stevani and Oliveira confirmed that this proposed reaction in a live fungi using “overlapping of light emission spectra” [34]. Several other authors also investigated the chemical process of bioluminescence in beetles [13,50] and in marine snails (limpets) and luminous bacteria [29,43]. In recent times, several works can be found with reference to fungal, bacterial, marine bioluminescence and bioluminescence in insects [6,12,15,24]. Kaskova et al. have recently reported the structure of fungal oxyluciferin and its mechanism [24]. In another interesting work, Fallon et al. have found a strong support for independent origin of luciferase (and so bioluminescence) between fireflies and click beetle, which provides new insights into the evolutionary path of these insects’ bioluminescence and their genes, chemical defenses, and symbionts [15]. The onset of bacterial bioluminescence and quenching through a dynamical model is presented by Delle et al. [44]. As far as the bioluminescence of
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