Vol.:(0123456789) 1 3 Modeling Earth Systems and Environment https://doi.org/10.1007/s40808-020-00884-w ORIGINAL ARTICLE Emergent impacts of alternative resource in cannibalistic predator–prey system Sukumar Samanta 1  · Banshidhar Sahoo 2  · Barun Das 1 Received: 16 April 2020 / Accepted: 8 July 2020 © Springer Nature Switzerland AG 2020 Abstract In this paper, a predator–prey model with cannibalistic effect in predator is presented. Naturally, juveniles predators are captured by their own adult predators in water population system. To reduce such conspecific capturing, alternative resource is supplied to adult predators as a supplementary food. The model is analyzed in terms of theoretical and numerical point of view. The conditions for local and global stability around existing equilibrium points, persistence, and Hopf bifurcation are derived theoretically. Numerical experiments illustrate that the extinction possibility of predator population can be reduced providing suitable alternative resources to adult predators. The impacts of alternative resource supply with the variation of other parameters are shown in the model. The dynamical relationship between the strength of cannibalism and alternative resource supply is also drawn. The model is useful specially in fishery system. Keywords Predator–prey · Cannibalism · Alternative resource · Persistence · Extinction · Hopf bifurcation Introduction Classical food chain system assumes that a species is homo- geneous and all individuals of a particular species occupy the same trophic level. In ecosystem, individuals of one spe- cies may be found in different trophic levels due to ontoge- netic changes in size. In particular, the dynamics of species interactions depend on species size–structure interactions (Persson 1999; Rudolf and Armstrong 2008). Individuals of a system undergo considerable size changes during their growth period. This size structure creates stage-structured species interactions (conspecific or heterospecific), in which the strength of interaction depends on relative stage of indi- viduals (Polis 1984). However, a stage-structured species interaction in ecosystem has become a broad area due to its ecological importance. The study on stage-structured preda- tor–prey models has been reported by so many scientists and researchers (Linley and Joseph 2004; Aiello Walter et al. 1992; Kumar et al. 2019). Cannibalism, which is the act of capturing and at least partial consumption of conspecifics, is ubiquitous in nature. It is a prevalent feature of stage-structured populations in both aquatic and terrestrial food chain systems. For an instance, in stage-structured cannibalism, where large indi- viduals consume, smaller conspecifics can be responsible for 8% (Belding’s ground squirrel) to 95% (dragonfly larvae) of the total mortality (Polis 1981; Chakraborty and Chatto- padhyay 2011). However, cannibalism has a strong impact on stage-structured predator–prey system, because it affects the behavioral changes among different stages of individuals (Sih 1981). It is well established in theoretical studies that cannibalism has an important effect on population structure and dynamics. Cannibalism is a common ecological interac- tion in the animal kingdom (Polis 1981; Elgar and Crespi 1992). Population models have been considered cannibal- istic effect in the system species showing strong stabiliz- ing effects. It can have either a stabilizing or a destabilizing effect on the predator–prey system. There are strong ecologi- cal evidences that cannibalism exists among prey as well as predator, yet this phenomenon has been less investigated (Sniegula et al. 2017; Choh et al. 2017; Prasad and Prasad * Sukumar Samanta sukumarvu@yahoo.com Banshidhar Sahoo banshivu@gmail.com Barun Das bdasskbu@gmail.com 1 Department of Applied Mathematics, S.K.B. University, Purulia, West Bengal, India 2 Department of Mathematics, Hiralal Bhakat College, Nalhati, Birbhum, West Bengal, India