Biological Conservation of Living Systems by Providing Additional Food Supplements in the Presence of Inhibitory Effect: A Theoretical Study Using Predator–Prey Models

Achieving Minimum-Time Biological Conservation and Pest Management for Additional Food provided Predator–Prey Systems involving Inhibitory Effect: A Qualitative Investigation

“…The outcomes of the studies (Srinivasu et al (2018a)) and (Vamsi et al (2019)) show that the dynamics of the system (2.7) -(2.8) depend on the dynamics of the initial system (2.3) -( 2.4) and nature of its isoclines. As in (Srinivasu et al (2018a)), we too consider the additional food provided to the initial system under the Condition I where the initial system does not admit any interior equilibria. We provide the summary of global dynamics of the additional food system under condition I in Appendix -A.…”

“…The predator-prey systems involving type IV functional response in the absence of additional food (called as initial system) and in the presence of additional food have been derived in (Srinivasu et al (2018a)). To make it easier for the reader to understand the later sections of this paper, in this section, we provide a glimpse of the dynamics of initial system and additional food provided system involving Type IV functional response as discussed in (Srinivasu et al (2018a)).…”

“…The predator-prey systems involving type IV functional response in the absence of additional food (called as initial system) and in the presence of additional food have been derived in (Srinivasu et al (2018a)). To make it easier for the reader to understand the later sections of this paper, in this section, we provide a glimpse of the dynamics of initial system and additional food provided system involving Type IV functional response as discussed in (Srinivasu et al (2018a)). For detailed analysis of stability of the equilibria admitted by both the systems and details of the local and global dynamics of the systems, readers are requested to refer to the works (Srinivasu et al (2018a); Vamsi et al ( 2019))…”

“…Recently, the authors in (Srinivasu et al (2018a)) and (Vamsi et al (2019)) have studied an additional food provided predator-prey system involving type IV functional response. Findings from these studies reveal that for an appropriate choice of quality and quantity of additional food, stable coexistence of both species can be achieved.…”

“…These findings are in accordance with the field outcomes presented in (Kozak et al (1994(Kozak et al ( , 1995; Putman and Staines (2004)) and (Winkler et al (2005)). Though the findings of (Srinivasu et al (2018a)) and (Vamsi et al (2019)) are very helpful in the context of biological conservation and bio-control, they may not be of good help in practical scenarios owing to their asymptotic nature. To overcome these limitations, we wish to study the controllability aspects of the additional food system involving type IV response in order to achieve the desired outcomes in minimum (finite) time.…”