Switching effect on the stability of the prey-predator system with three trophic levels

1986 ◽  
Vol 122 (3) ◽  
pp. 251-262 ◽  
Author(s):  
Hiroyuki Matsuda ◽  
Kohkichi Kawasaki ◽  
Nanako Shigesada ◽  
Ei Teramoto ◽  
Luigi M. Ricciardi
Keyword(s):  
Trophic Levels ◽  
Switching Effect ◽  
The Stability ◽  
Predator System

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals Fishing effects on elasmobranchs from the Pacific Coast of Colombia

2016 ◽  
Vol 21 (1) ◽  
pp. 9 ◽  
Author(s):  
Andrés Felipe Navia ◽  
Paola Andrea Mejía-Falla
Keyword(s):  
Species Composition ◽  
Pacific Coast ◽  
Trophic Levels ◽  
Functional Level ◽  
The Pacific ◽  
The Mean ◽  
The Stability ◽  
Large Predators ◽  
Average Catch ◽  
Index Of Diversity

<p>During 1995, 2001, 2003, 2004 and 2007; we studied the temporal variation in the structure of the elasmobranch assemblage along the Colombian Pacific coast using: the community index of diversity, heterogeneity, equitability, species composition, average catch sizes, and mean trophic levels. A total of 1 711 specimens from 19 species<br />(7 sharks and 12 rays) were collected during the 90 trawling operations. The number of species captured varied between 7 (1995) and 12 (2007) demonstrating a trend towards an imbalance in the assemblage attributes. In 1995, the mean trophic level (TLm) of the assemblage was 3.60, but in 2007 it decreased to 3.55 when the functional level of large predators was absent (TL ≥ 4). These results suggest changes in species composition, structural attributes, and a reduction of the highest functional level. Alterations to the catch proportions were also found: i.e. a greater abundance of rays of lower trophic levels. This study suggests an effect of trawling on the stability of this tropical coastal ecosystem.</p>

scholarly journals Loss of top-down biotic interactions changes the relative benefits for obligate mutualists

2019 ◽  
Vol 286 (1897) ◽  
pp. 20182501 ◽  
Author(s):  
Rong Wang ◽  
Xiao-Yong Chen ◽  
Yan Chen ◽  
Gang Wang ◽  
Derek W. Dunn ◽  
...  
Keyword(s):  
Biotic Interactions ◽  
Trophic Levels ◽  
Fig Wasp ◽  
Negative Effects ◽  
Top Down ◽  
Top Predators ◽  
Natural Range ◽  
Obligate Mutualism ◽  
The Stability ◽  
Food Web Complexity

The collapse of mutualisms owing to anthropogenic changes is contributing to losses of biodiversity. Top predators can regulate biotic interactions between species at lower trophic levels and may contribute to the stability of such mutualisms, but they are particularly likely to be lost after disturbance of communities. We focused on the mutualism between the fig tree Ficus microcarpa and its host-specific pollinator fig wasp and compared the benefits accrued by the mutualists in natural and translocated areas of distribution. Parasitoids of the pollinator were rare or absent outside the natural range of the mutualists, where the relative benefits the mutualists gained from their interaction were changed significantly away from the plant's natural range owing to reduced seed production rather than increased numbers of pollinator offspring. Furthermore, in the absence of the negative effects of its parasitoids, we detected an oviposition range expansion by the pollinator, with the use of a wider range of ovules that could otherwise have generated seeds. Loss of top-down control has therefore resulted in a change in the balance of reciprocal benefits that underpins this obligate mutualism, emphasizing the value of maintaining food web complexity in the Anthropocene.

scholarly journals Stability and Hopf Bifurcation Analysis on a Bazykin Model with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianming Zhang ◽  
Lijun Zhang ◽  
Chaudry Masood Khalique
Keyword(s):  
Hopf Bifurcation ◽  
Normal Form ◽  
Periodic Solutions ◽  
Bifurcation Analysis ◽  
Center Manifold ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Finite Delay ◽  
The Stability ◽  
Predator System

The dynamics of a prey-predator system with a finite delay is investigated. We show that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases. By using the theory of normal form and center manifold, explicit expressions for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.

STABILITY ANALYSIS OF A PREY-PREDATOR MODEL WITH DELAY AND HARVESTING

2004 ◽  
Vol 12 (01) ◽  
pp. 61-71 ◽  
Author(s):  
TAPAN KUMAR KAR
Keyword(s):  
Stability Analysis ◽  
Computer Simulations ◽  
Significant Role ◽  
Combined Effects ◽  
Predator Model ◽  
The Stability ◽  
Predator System

An analysis is presented for a model of a two species prey-predator system subject to the combined effects of delay and harvesting. Our study shows that, both the delay and harvesting effort may play a significant role on the stability of the system. Computer simulations are carried out to explain some of the mathematical conclusions.

scholarly journals Scrounging by foragers can resolve the paradox of enrichment

2016 ◽  
Author(s):  
Wataru Toyokawa
Keyword(s):  
Group Living ◽  
Theoretical Models ◽  
Social Foraging ◽  
Predator Population ◽  
Ecological Communities ◽  
Predator Prey ◽  
Paradox Of Enrichment ◽  
Prey System ◽  
The Stability ◽  
Predator System

AbstractTheoretical models of predator-prey system predict that sufficient enrichment of prey can generate large amplitude limit cycles, paradoxically causing a high risk of extinction (the paradox of enrichment). While real ecological communities contain many gregarious species whose foraging behaviour should be influenced by socially transmitted information, few theoretical studies have examined the possibility that social foraging might be a resolution of the paradox. I considered a predator population in which individuals play the producer-scrounger foraging game both in a one-prey-one-predator system and a two-prey-one-predator system. I analysed the stability of a coexisting equilibrium point in the former one-prey system and that of non-equilibrium dynamics of the latter two-prey system. The result showed that social foraging can stabilise both systems and thereby resolves the paradox of enrichment when scrounging behaviour is prevalent in predators. This suggests a previously neglected mechanism underlying a powerful effect of group-living animals on sustainability of ecological communities.

scholarly journals Effect of time delay on a detritus-based ecosystem

2006 ◽  
Vol 2006 ◽  
pp. 1-28 ◽  
Author(s):  
Nurul Huda Gazi ◽  
Malay Bandyopadhyay
Keyword(s):  
Time Delay ◽  
Equilibrium Points ◽  
Equation Model ◽  
Model System ◽  
Trophic Levels ◽  
Dynamical Analysis ◽  
Discrete Time Delay ◽  
Growth Equations ◽  
The Stability ◽  
Delay Differential

Models of detritus-based ecosystems with delay have received a great deal of attention for the last few decades. This paper deals with the dynamical analysis of a nonlinear model of a detritus-based ecosystem involving detritivores and predator of detritivores. We have obtained the criteria for local stability of various equilibrium points and persistence of the model system. Next, we have introduced discrete time delay due to recycling of dead organic matters and gestation of nutrients to the growth equations of various trophic levels. With delay differential equation model system we have studied the effect of time delay on the stability behaviour. Next, we have obtained an estimate for the length of time delay to preserve the stability of the model system. Finally, the existence of Hopf-bifurcating small amplitude periodic solutions is derived by considering time delay as a bifurcation parameter.

scholarly journals Trophodynamics and stability of regional scale ecosystems in the Northeast Atlantic

2012 ◽  
Vol 69 (5) ◽  
pp. 764-775 ◽  
Author(s):  
Niall McGinty ◽  
Anne Marie Power ◽  
Mark P. Johnson
Keyword(s):  
Control Charts ◽  
Marine Ecosystem ◽  
Regional Scale ◽  
Trophic Levels ◽  
Northeast Atlantic ◽  
Long Term Stability ◽  
Large Marine Ecosystem ◽  
Trends Over Time ◽  
The Stability ◽  
Multivariate Control

Abstract McGinty, N., Power, A. M., and Johnson, M. P. 2012. Trophodynamics and stability of regional scale ecosystems in the Northeast Atlantic. – ICES Journal of Marine Science, 69: 764–775. This study addresses the long-term stability of three trophic groupings in the Northeast Atlantic at regional scales. The most abundant taxa representing phytoplankton, herbivorous copepods, and carnivorous zooplankton were examined from the Continuous Plankton Recorder database. Multivariate control charts using a Bray–Curtis similarity metric were used to assess whether fluctuations within trophic groupings were within or beyond the expected variability. Two evaluation periods were examined: annual changes between 1960 and 1999 (2000–2009 baseline) and recent changes between 2000 and 2009 (1960–1999 baseline). The trends over time in abundance/biomass of trophic levels were region-specific, especially in carnivorous copepods, where abundance did not mirror trends in the overall study area. The stability of phytoplankton was within the expected limits, although not in 2008 and 2009. Higher trophic levels were less stable, perhaps reflecting the added complexity of interactions governing their abundance. In addition, some regions were consistently less stable than others. Correlations in stability between adjacent trophic levels were positive at large marine ecosystem scale but generally non-significant at regional scales. The study suggests that certain regions may be particularly vulnerable to periods of instability in community structure. The benefits of using the control chart method rather than other multivariate measures of plankton dynamics are discussed.

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