strong allee effect
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2021 ◽  
Author(s):  
Asim Sikder

Abstract We consider a Gause-type prey-predator system incorporating a strong allee effect for the prey population. For the existence of multiple interior equilibria we consider Holling-type predator functional response and the density dependent death rate for the predator. With the help of the Conley connection matrix theory we study the dynamics of the system in presence of one, two and three interior equilibria. It is found that (i) the saddle-saddle connections exist in presence of single and multiple interior equilibria connecting interior flows to the boundary and (ii) the system admits a set of degree-2 (i.e, a 2-discs of) connecting orbits from interior equlibrium to the origin. Thus permanence or robust permanence of the system is not possible.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Deeptajyoti Sen ◽  
Sudeshna Sinha

AbstractWe consider the dynamics of a three-species system incorporating the Allee Effect, focussing on its influence on the emergence of extreme events in the system. First we find that under Allee effect the regular periodic dynamics changes to chaotic. Further, we find that the system exhibits unbounded growth in the vegetation population after a critical value of the Allee parameter. The most significant finding is the observation of a critical Allee parameter beyond which the probability of obtaining extreme events becomes non-zero for all three population densities. Though the emergence of extreme events in the predator population is not affected much by the Allee effect, the prey population shows a sharp increase in the probability of obtaining extreme events after a threshold value of the Allee parameter, and the vegetation population also yields extreme events for sufficiently strong Allee effect. Lastly we consider the influence of additive noise on extreme events. First, we find that noise tames the unbounded vegetation growth induced by Allee effect. More interestingly, we demonstrate that stochasticity drastically diminishes the probability of extreme events in all three populations. In fact for sufficiently high noise, we do not observe any more extreme events in the system. This suggests that noise can mitigate extreme events, and has potentially important bearing on the observability of extreme events in naturally occurring systems.


2021 ◽  
Vol 2068 (1) ◽  
pp. 012044
Author(s):  
Jiao Ai ◽  
Kaihua Wang

Abstract With periodic coefficients and strong Allee effects, we establish a delayed intraguild predation impulsive model. We obtain a set of sufficient conditions for the existence of positive periodic solution of the model using Mawhin’s continuation theorem and analysis techniques. Finally, we identify the effectiveness of the theoretical results through some numerical simulations.


2021 ◽  
pp. 3114-3127
Author(s):  
Saad M. A. Al-Momen ◽  
Raid Kamil Naji

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jingwen Zhu ◽  
Ranchao Wu ◽  
Mengxin Chen

Abstract In this paper, strong Allee effects on the bifurcation of the predator–prey model with ratio-dependent Holling type III response are considered, where the prey in the model is subject to a strong Allee effect. The existence and stability of equilibria and the detailed behavior of possible bifurcations are discussed. Specifically, the existence of saddle-node bifurcation is analyzed by using Sotomayor’s theorem, the direction of Hopf bifurcation is determined, with two bifurcation parameters, the occurrence of Bogdanov–Takens of codimension 2 is showed through calculation of the universal unfolding near the cusp. Comparing with the cases with a weak Allee effect and no Allee effect, the results show that the Allee effect plays a significant role in determining the stability and bifurcation phenomena of the model. It favors the coexistence of the predator and prey, can lead to more complex dynamical behaviors, not only the saddle-node bifurcation but also Bogdanov–Takens bifurcation. Numerical simulations and phase portraits are also given to verify our theoretical analysis.


2021 ◽  
Author(s):  
Gergely Röst ◽  
AmirHosein Sadeghimanesh

In this note we consider two populations living on identical patches, connected by unidirectional migration, and subject to strong Allee effect. We show that by increasing the migration rate, there are more bifurcation sequences than previous works showed. In particular, the number of steady states can change from 9 (small migration) to 3 (large migration) at a single bifurcation point, or via a sequences of bifurcations with the system having 9,7,5,3 or 9,7,9,3 steady states, depending on the Allee threshold. This is in contrast with the case of bidirectional migration, where the number of steady states always goes through the same bifurcation sequence of 9,5,3 steady states as we increase the migration rate, regardless of the value of the Allee threshold.


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