scholarly journals Evaluating the precariousness of coral recovery when coral and macroalgae are alternative basins of attraction

2021 ◽  
Author(s):  
Russell J. Schmitt ◽  
Sally J. Holbrook ◽  
Andrew J. Brooks ◽  
Thomas C. Adam
Keyword(s):  
Basins Of Attraction ◽  
Coral Recovery

scholarly journals Nonlinear Compartment Models with Time-Dependent Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1657
Author(s):  
Jochen Merker ◽  
Benjamin Kunsch ◽  
Gregor Schuldt
Keyword(s):  
Stable Equilibrium ◽  
Compartment Model ◽  
Basins Of Attraction ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Compartment Models ◽  
Autonomous Case ◽  
Hyperbolic Equilibrium ◽  
Interior Points ◽  
Two Parameter

A nonlinear compartment model generates a semi-process on a simplex and may have an arbitrarily complex dynamical behaviour in the interior of the simplex. Nonetheless, in applications nonlinear compartment models often have a unique asymptotically stable equilibrium attracting all interior points. Further, the convergence to this equilibrium is often wave-like and related to slow dynamics near a second hyperbolic equilibrium on the boundary. We discuss a generic two-parameter bifurcation of this equilibrium at a corner of the simplex, which leads to such dynamics, and explain the wave-like convergence as an artifact of a non-smooth nearby system in C0-topology, where the second equilibrium on the boundary attracts an open interior set of the simplex. As such nearby idealized systems have two disjoint basins of attraction, they are able to show rate-induced tipping in the non-autonomous case of time-dependent parameters, and induce phenomena in the original systems like, e.g., avoiding a wave by quickly varying parameters. Thus, this article reports a quite unexpected path, how rate-induced tipping can occur in nonlinear compartment models.

scholarly journals Assessing population collapse of Drupella spp. (Mollusca: Gastropoda) 2 years after a coral bleaching event in the Republic of Maldives

Hydrobiologia ◽  
2021 ◽  
Author(s):  
L. Saponari ◽  
I. Dehnert ◽  
P. Galli ◽  
S. Montano
Keyword(s):  
Coral Bleaching ◽  
Prey Availability ◽  
Coral Cover ◽  
Environmental Data ◽  
High Plasticity ◽  
Bleaching Event ◽  
Coral Recovery ◽  
The Republic ◽  
The Impact ◽  
Line Intercept

AbstractCorallivory causes considerable damage to coral reefs and can exacerbate other disturbances. Among coral predators, Drupella spp. are considered as delayer of coral recovery in the Republic of Maldives, although little information is available on their ecology. Thus, we aimed to assess their population structure, feeding behaviour and spatial distribution around 2 years after a coral bleaching event in 2016. Biological and environmental data were collected using belt and line intercept transects in six shallow reefs in Maldives. The snails occurred in aggregations with a maximum of 62 individuals and exhibited a preference for branching corals. Yet, the gastropods showed a high plasticity in adapting feeding preferences to prey availability. Drupella spp. were homogenously distributed in the study area with an average of 9.04 ± 19.72 ind/200 m2. However, their occurrence was significantly different at the reef scale with the highest densities found in locations with higher coral cover. The impact of Drupella spp. appeared to be minimal with the population suffering from the loss of coral cover. We suggest that monitoring programs collect temporal- and spatial-scale data on non-outbreaking populations or non-aggregating populations to understand the dynamics of predation related to the co-occurrence of anthropogenic and natural impacts.

scholarly journals A Characterization of the Dynamics of Schröder’s Method for Polynomials with Two Roots

2021 ◽  
Vol 5 (1) ◽  
pp. 25
Author(s):  
Víctor Galilea ◽  
José M. Gutiérrez
Keyword(s):  
Nonlinear Equations ◽  
Complex Plane ◽  
Iterative Process ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Schröder’S Method

The purpose of this work is to give a first approach to the dynamical behavior of Schröder’s method, a well-known iterative process for solving nonlinear equations. In this context, we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder’s method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We conclude our study with a graphical gallery that allow us to compare the basins of attraction of Newton’s and Schröder’s method applied to some given polynomials.

scholarly journals Doom and Boom on a Resilient Reef: Climate Change, Algal Overgrowth and Coral Recovery

PLoS ONE ◽  
2009 ◽  
Vol 4 (4) ◽  
pp. e5239 ◽  
Author(s):  
Guillermo Diaz-Pulido ◽  
Laurence J. McCook ◽  
Sophie Dove ◽  
Ray Berkelmans ◽  
George Roff ◽  
...  
Keyword(s):  
Climate Change ◽  
Coral Recovery

BASIN CONFIGURATION OF A SIX-DIMENSIONAL MODEL OF AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 1333-1356 ◽  
Author(s):  
YOSHISUKE UEDA ◽  
HIROYUKI AMANO ◽  
RALPH H. ABRAHAM ◽  
H. BRUCE STEWART
Keyword(s):  
Power Systems ◽  
Power System ◽  
Initial Conditions ◽  
Electrical Power ◽  
Practical Importance ◽  
Intervention Strategy ◽  
Basins Of Attraction ◽  
Electric Power System ◽  
Point Of View ◽  
Electrical Power System

As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. This system represents a simple model of an electrical power system involving three machines and an infinite bus. Apart from the possible occurrence of attractors representing pathological states, the contacts between the basins have a practical importance, from the point of view of the operation of a real electrical power system. With the aid of a global map of basins, one could hope to design an intervention strategy to boot the power system back into its normal state. Our method involves taking two-dimensional sections of the six-dimensional state space, and then determining the basins directly by numerical simulation from a dense grid of initial conditions. The relations among all the basins are given for a specific numerical example, that is, choosing particular values for the parameters in our model.

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

THE EFFECT OF SEASONAL HARVESTING ON A STAGE-STRUCTURED DISCRETE MODEL WITH BIRTH PULSES

2006 ◽  
Vol 16 (09) ◽  
pp. 2575-2586 ◽  
Author(s):  
SHUJING GAO ◽  
LANSUN CHEN
Keyword(s):  
Single Pulse ◽  
Stage Structure ◽  
Single Species ◽  
Fish Population ◽  
Basins Of Attraction ◽  
Fish Stock ◽  
Strong Impact ◽  
Natural Period ◽  
Discrete Population ◽  
Mature Fish

In this paper, we propose an exploited single-species discrete population model with stage structure for the dynamics in a fish population for which births occur in a single pulse once per time period. Using the stroboscopic map, we obtain an exact cycle of the system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate (or harvesting effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, pitchfork and tangent bifurcation, nonunique dynamics (meaning that several attractors or attractor and chaos coexist), basins of attraction and attractor crisis. This suggests that birth pulse provides a natural period or cyclicity that makes the dynamical behaviors more complex. Moreover, we show that the timing of harvesting has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. An interesting result is obtained that, after the birth pulses, the population can sustain much higher harvesting effort if the mature fish is removed as early in the season as possible.

Sign in / Sign up

Export Citation Format

Share Document