Black swans and canards in two predator – one prey model

2019 ◽  
Vol 14 (4) ◽  
pp. 408 ◽  
Author(s):  
Elena Shchepakina
Keyword(s):  
Invariant Manifold ◽  
Black Swan ◽  
Black Swans ◽  
Prey Model ◽  
Slow Invariant Manifold

In this paper, we show how canards can be easily caught in a class of 3D systems with an exact black swan (a slow invariant manifold of variable stability). We demonstrate this approach to a canard chase via the two predator – one prey model. It is shown that the technique described allows us to get various 3D oscillations by changing the shape of the trajectories of two 2D-projections of the original 3D system.

Slow invariant manifold assessments in multi-route reaction mechanism

2019 ◽  
Vol 284 ◽  
pp. 265-270 ◽  
Author(s):  
M. Shahzad ◽  
F. Sultan ◽  
M. Ali ◽  
W.A. Khan ◽  
M. Irfan
Keyword(s):  
Reaction Mechanism ◽  
Invariant Manifold ◽  
Slow Invariant Manifold

scholarly journals The reaction routes comparison with respect to slow invariant manifold and equilibrium points

AIP Advances ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 015212 ◽  
Author(s):  
Faisal Sultan ◽  
Muhammad Shahzad ◽  
Mehboob Ali ◽  
Waqar Azeem Khan
Keyword(s):  
Invariant Manifold ◽  
Equilibrium Points ◽  
Slow Invariant Manifold ◽  
Reaction Routes

scholarly journals The Effect of Slow Invariant Manifold and Slow Flow Dynamics on the Energy Transfer and Dissipation of a Singular Damped System with an Essential Nonlinear Attachment

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jamal-Odysseas Maaita ◽  
Efthymia Meletlidou
Keyword(s):  
Energy Transfer ◽  
Total Energy ◽  
Invariant Manifold ◽  
Nonlinear Oscillator ◽  
Invariant Manifolds ◽  
Dissipative System ◽  
Flow Dynamics ◽  
Slow Flow ◽  
Damped System ◽  
Slow Invariant Manifold

We study the effect of slow flow dynamics and slow invariant manifolds on the energy transfer and dissipation of a dissipative system of two linear oscillators coupled with an essential nonlinear oscillator with a mass much smaller than the masses of the linear oscillators. We calculate the slow flow of the system, the slow invariant manifold, the total energy of the system, and the energy that is stored in the nonlinear oscillator for different sets of the parameters and show that the bifurcations of the SIM and the dynamics of the slow flow play an important role in the energy transfer from the linear to the nonlinear oscillator and the rate of dissipation of the total energy of the initial system.

THE SLOW INVARIANT MANIFOLD OF A CONSERVATIVE PENDULUM-OSCILLATOR SYSTEM

1996 ◽  
Vol 06 (04) ◽  
pp. 673-692 ◽  
Author(s):  
IOANNIS T. GEORGIOU ◽  
IRA B. SCHWARTZ
Keyword(s):  
Invariant Manifold ◽  
Invariant Manifolds ◽  
Slow Manifold ◽  
Equilibrium States ◽  
Periodic Motions ◽  
Nonlinear Normal Mode ◽  
Oscillator System ◽  
Slow Invariant Manifold ◽  
Nonlinear Normal ◽  
Global Invariant

We analyze the motions of a conservative pendulum-oscillator system in the context of invariant manifolds of motion. Using the singular perturbation methodology, we show that whenever the natural frequency of the oscillator is sufficiently larger than that of the pendulum, there exists a global invariant manifold passing through all static equilibrium states and tangent to the linear eigenspaces at these equilibrium states. The invariant manifold, called slow, carries a continuum of slow periodic motions, both oscillatory and rotational. Computations to various orders of approximation to the slow invariant manifold allow analysis of motions on the slow manifold, which are verified with numerical experiments. Motion on the slow invariant manifold is identified with a slow nonlinear normal mode.

scholarly journals Aspects of the Feeding Ecology of Mallard and Black Swan in a Small Freshwater Lake

2021 ◽  
Author(s):  
◽  
Kerry John Potts
Keyword(s):  
New Zealand ◽  
Feeding Ecology ◽  
Food Supply ◽  
Freshwater Lake ◽  
Reserve Capacity ◽  
Black Swan ◽  
Feeding Patterns ◽  
Black Swans ◽  
Wetland Complex ◽  
Food Content

<p>Section 1. Limnological and waterfowl food supply characteristics of Pukepuke Lagoon are described. Emphasis is placed on describing how the balance between macrophytes and phytoplankton is established (these two forms of vegetation tend to dominate alternately in the lagoon). The question of whether heavy swan grazing may potentially shift this balance in favour of phytoplankton dominance is examined. Section 2. The year-round patterns of feeding exhibited by mallards are described on the basis of scan counts taken at one or two-hourly intervals from dawn to dusk. These feeding patterns, graphically depicted, are then interpreted and discussed against the background of what is known of the food content of the lagoon. Reference is made to the behavioural and physiological adaptability of the birds, and to the reserve capacity of the wetland complex - not just Pukepuke Lagoon - to sustain them. The relevance of these findings and interpretations, to New Zealand in general is discussed. Section 3. An hypothesis is developed to account for the way in which black swans use various waters in the Pukepuke-centred wetland complex.</p>

scholarly journals Decision-Making in Rats is Sensitive to Rare and Extreme Events: the Black Swan Avoidance

2021 ◽  
Author(s):  
Mickael Degoulet ◽  
Louis-Mattis Willem ◽  
Christelle Baunez ◽  
Stephane Luchini ◽  
Patrick Pintus
Keyword(s):  
Decision Making ◽  
Experimental Design ◽  
Extreme Events ◽  
Decision Making Under Uncertainty ◽  
Black Swan ◽  
Black Swans ◽  
Time Out ◽  
Radical Uncertainty

Most studies assessing decision-making under uncertainty use events with probabilities that are above 10-20 %. Here, to study decision-making in radical uncertainty conditions, Degoulet, Willem, Baunez, Luchini and Pintus provide a novel experimental design that aims at measuring the extent to which rats are sensitive - and how they respond - to extremely rare (below 1% of probability) but extreme events in a four-armed bandit task. Gains (sugar pellets) and losses (time-out punishments) are such that large - but rare - values materialize or not depending on the option chosen. The results show that all rats diversify their choices across options. However, most rats exhibit sensitivity to rare and extreme events despite their sparse occurrence, by combining more often options with extreme gains (Jackpots) and/or avoidance of extreme losses (Black Swans). In general, most rats choices feature one-sided sensitivity in favor of trying more often to avoid extreme losses than to seek extreme gains - that is, they feature Black Swan Avoidance.

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