Stability of a certain class of a host–parasitoid models with a spatial refuge effect

Bešo, Emin; Kalabušić, Senada; Mujić, Naida; Pilav, Esmir

doi:10.1080/17513758.2019.1692916

Cited by 23 publications

(13 citation statements)

References 24 publications

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“…Much work has identified two orthogonal mechanisms by which stability can arise in these discrete-time models: The first mechanism is when the escape response f ( P t ) only depends on the parasitoid density, and then the non-trivial host-parasitoid equilibrium is stable, if and only, if, the equilibrium adult host density is an increasing function of the host reproduction rate R [9]. This type of stability arises through several related processes, such as, a fraction of the host population being in a refuge (i.e., protected from parasitoid attacks) [3], [10], large host-to-host difference in parasitism risk [9], [11]–[13], parasitoid interference [14]–[16], and aggregation in parasitoid attacks [17]–[19]. The second mechanism is a Type III functional response where the parasitoid attack rate accelerates sufficiently rapidly with increasing host density [20].…”

Section: Introductionmentioning

confidence: 99%

Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

Singh

2021

Preprint

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Population dynamics of host-parasitoid interactions has been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

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Section: Introductionmentioning

confidence: 99%

Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

Singh

2021

Preprint

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“…For some other notable modifications in host-parasitoid interaction, we refer to [5][6][7][8][9][10][11][12][13][14][15][16][17] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A class of discrete predator–prey interaction with bifurcation analysis and chaos control

Din

Saleem

Shabbir

2020

Math. Model. Nat. Phenom.

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The interaction between prey and predator is well--known within natural ecosystems. Due to their multifariousness and strong link population dynamics, predators contain distinct features of ecological communities. Keeping in view the Nicholson-Bailey framework for host-parasitoid interaction, a discrete-time predator-prey system is formulated and studied with implementation of type--II functional response and logistic prey growth in form of the Beverton-Holt map. Persistence of solutions and existence of equilibria are discussed. Moreover, stability analysis of equilibria is carried out for predator-prey model. With implementation of bifurcation theory of normal forms and center manifold theorem, it is proved that system undergoes transcritical bifurcation around its boundary equilibrium. On the other hand, if growth rate of consumers is taken as bifurcation parameter, then system undergoes Neimark-Sacker bifurcation around its positive equilibrium point. Methods of chaos control are introduced to avoid the populations from unpredictable behavior. Numerical simulation is provided to strengthen our theoretical discussion.

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“…Moreover, in [19], chaos control and bifurcation analysis were studied for a host-parasitoid model with a lower bound for the host. In [20] and [21], the influence of a refuge effect was explored for certain classes of host-parasitoid models. In [22], the authors numerically investigated a system of partial differential equations that describe the interactions between populations of predators and prey.…”

Section: Introductionmentioning

confidence: 99%

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

Ma¹,

Din

Rafaqat

et al. 2020

Mathematics

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The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations.

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Stability of a certain class of a host–parasitoid models with a spatial refuge effect

Cited by 23 publications

References 24 publications

Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

A class of discrete predator–prey interaction with bifurcation analysis and chaos control

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

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