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Usually, juvenile predators are small in size, comparatively feeble and in the earlier phase of learning the tricky manoeuvre skills of predation. Due to small prey-predator size-ratio, juvenile predators and preys become two deadliest opponents, therefore, whenever both face off, the outcome may be utterly unpredictable. In response to the juvenile predators' attack, preys also come up with a countermeasure and try to defend themselves but a sharp role-reversal in the predator-prey ecology occurs when preys kill the juvenile predators during the counter-attacking strategies. In this paper, we propose and analyze a biologically motivated delayed predator-prey system to explore the joint impact of counterattacking strategies and multiple delays on the predator-prey interactions. We have introduced the transformation of immature to mature predators including delay τ 1 as an average time to reach maturity. Another time delay τ 2 owing to the gestation of the adult predators, is taken into account. After the brief discussion of the basic ecosystem properties for the model in absence of delay, we have performed the stability analysis of the delayed system comprehensively. In this context, existence of Hopf bifurcation at the interior equilibrium is established and its stability as well as direction of the Hopf bifurcation is also investigated. Numerical simulations are also performed to corroborate the theoretical findings. Through this work, it has been illustrated that counterattacking of preys suppresses the unstable oscillations in the population, on the other hand, large delays always destabilize the interior steady state. Hence, in the realistic predator-prey ecology, where counterattack and delays are showing opposite behavior in the same ecosystem, the results of this paper are important to disclose the actual crossover and synergies between both the ecological properties.

Bachelor herd behavior is very common among juvenile animals who have not become sexually matured but have left their parent groups. The complex grouping or schooling behavior provides vulnerable juveniles refuge from predation and opportunities for foraging, especially when their parents are not within the area to protect them. In spite of this, juvenile/immature prey may easily become victims because of their greenness while on the other hand, adult prey may be invulnerable to attack due to their tricky manoeuvring abilities to escape from the predators. In this study, we propose a stage-structured predator–prey model, in which predators attack only the bachelor herds of juvenile prey while adult prey save themselves due to small predator–prey size ratio and their fleeing capability, enabling them to avoid confrontation with the predators. Local and global stability analysis on the equilibrium points of the model are performed. Sufficient conditions for uniform permanence and the impermanence are derived. The model exhibits both transcritical as well as Hopf bifurcations and the corresponding numerical simulations are carried out to support the analytical results. Bachelor herding of juvenile prey as well as inaccessibility of adult prey restricts the uncontrolled predation so that prey abundance and predation remain balanced. This investigation on bachelor group defence brings out some unpredictable results, especially close to the zero steady state. Altogether, bachelor herding of the juvenile prey, which causes unconventional behavior near the origin, plays a significant role in establishing uniform permanence conditions, also increases richness of the dynamics in numerical simulations using the bifurcation theory and thereby, shapes ecosystem properties tremendously and may have a large influence on the ecosystem functioning.

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