scholarly journals Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress

2017 ◽  
Vol 14 (128) ◽  
pp. 20160845 ◽  
Author(s):  
Vasilis Dakos ◽  
Sarah M. Glaser ◽  
Chih-hao Hsieh ◽  
George Sugihara
Keyword(s):  
Nonlinear Models ◽  
Type Model ◽  
Forecast Performance ◽  
Economic Implications ◽  
Equilibrium Dynamics ◽  
Abrupt Changes ◽  
Local Extinctions ◽  
Abrupt Shifts ◽  
The Stability ◽  
Dynamics Of Populations

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom–bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress.

scholarly journals Elevated nonlinearity as indicator of transition to overexploitation in fish stocks

2016 ◽  
Author(s):  
Vasilis Dakos ◽  
Sarah M. Glaser ◽  
Chih-hao Hsieh ◽  
George Sugihara
Keyword(s):  
Trophic Structure ◽  
Type Model ◽  
Western Atlantic ◽  
Economic Implications ◽  
Fish Stocks ◽  
As Species ◽  
Abrupt Changes ◽  
Risk Of Extinction ◽  
Statistical Metrics

AbstractEcosystems may experience abrupt changes such as species extinctions, reorganisations of trophic structure, or transitions from stable population dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we use a Ricker-type model to simulate the transition of a hypothetical stable fisheries population either to irregular boom-bust dynamics or to overexploitation. Our aim is to infer the risk of extinction in these two scenarios by comparing changes in variance, autocorrelation, and nonlinearity between unexploited and exploited populations. We find that changes in these statistical metrics reflect the risk of extinction but depend on the type of dynamical transition. Variance and nonlinearity increase similarly in magnitude along both transitions. In contrast, autocorrelation depends strongly on the presence of underlying oscillating dynamics. We also compare our theoretical expectations to indicators measured in long-term datasets of fish stocks from the California Cooperative Oceanic Fisheries Investigation in the Eastern Pacific and from the Northeast Shelf in the Western Atlantic. Our results suggest that elevated variance and nonlinearity could be potentially used to rank exploited fish populations according to their risk of extinction.

scholarly journals Assessing the Impacts of Competition and Dispersal on a Multiple Interactions Type Model

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Murtala Bello Aliyu ◽  
Mohd Hafiz Mohd ◽  
Mohd Salmi Md. Noorani
Keyword(s):  
Bifurcation Analysis ◽  
Species Coexistence ◽  
Real Life ◽  
Period Doubling ◽  
Type Model ◽  
Coexistence Mechanisms ◽  
Multiple Species ◽  
The Stability ◽  
Transcritical Bifurcations ◽  
Multiple Interactions

Multiple interactions (e.g., mutualist-resource-competitor-exploiter interactions) type models are known to exhibit oscillatory behaviour as a result of their complexity. This large-amplitude oscillation often de-stabilises multispecies communities and increases the chances of species extinction. What mechanisms help species in a complex ecological system to persist? Some studies show that dispersal can stabilise an ecological community and permit multi-species coexistence. However, previous empirical and theoretical studies often focused on one- or two-species systems, and in real life, we have more than two-species coexisting together in nature. Here, we employ a (four-species) multiple interactions type model to investigate how competition interacts with other biotic factors and dispersal to shape multi-species communities. Our results reveal that dispersal has (de-)stabilising effects on the formation of multi-species communities, and this phenomenon shapes coexistence mechanisms of interacting species. These contrasting effects of dispersal can best be illustrated through its combined influences with the competition. To do this, we employ numerical simulation and bifurcation analysis techniques to track the stable and unstable attractors of the system. Results show the presence of Hopf bifurcations, transcritical bifurcations, period-doubling bifurcations and limit point bifurcations of cycles as we vary the competitive strength in the system. Furthermore, our bifurcation analysis findings show that stable coexistence of multiple species is possible for some threshold values of ecologically-relevant parameters in this complex system. Overall, we discover that the stability and coexistence mechanisms of multiple species depend greatly on the interplay between competition, other biotic components and dispersal in multi-species ecological systems.

scholarly journals On resolution of the method of directional magnetotelluric soundings

2015 ◽  
Vol 1 (4) ◽  
pp. 82-85
Author(s):  
Михаил Савин ◽  
Mihail Savin
Keyword(s):  
Field Measurement ◽  
Measurement Errors ◽  
Prediction Modeling ◽  
Mathematical Experiment ◽  
Magnetotelluric Soundings ◽  
Geoelectric Model ◽  
Stability Of Solution ◽  
Abrupt Changes ◽  
The Stability ◽  
Electric Mode

The problem is to examine the resolution of directional magnetotelluric soundings (DMTS). Abrupt changes of impedances of electrical and magnetic types in critical region of parameters R~0, J~ωµσ are shown to result in significantly higher resolution of the method as compared with the traditional interpretation using Tikhonov–Cagniard impedance. The stability of solution of DMTS method inverse problem is considered subject to field measurement errors limited the resolution. The minimum of the limits is determined for the conductivity ∆σ/σ small variations. For studying DMTS resolution as applied to MT monitoring of earthquake site the mathematical experiment for three-layer geoelectric model was carried out. When changing the earthquake site conductivity of ∆σ~±10 % variations of reflection coefficient of electric mode are in the range of 20 % that is significantly more than the field measurement error. The possibility for prediction modeling in the context of obtained results is discussed.

Effect of Reactant Preheating on the Stability of Non-Premixed Methane/Air Flames

2010 ◽  
Author(s):  
Sylvain Lamige ◽  
Ce´dric Galizzi ◽  
Jiesheng Min ◽  
Julien Perles ◽  
Fre´de´ric Andre´ ◽  
...  
Keyword(s):  
Room Temperature ◽  
Initial Temperature ◽  
Flame Stability ◽  
Air Velocity ◽  
Lifted Flames ◽  
Local Extinctions ◽  
Lift Off ◽  
Temperature Levels ◽  
The Stability ◽  
Jet Velocities

This study details the influence of reactant temperature on the stability of non-premixed CH4/air co-flow jet flames. Flame characteristics have been studied for five temperature levels (from 295 K to 600 K). The hysteresis zone formed by the limits between attached and lifted flame translates towards higher methane jet velocities with an increase of initial temperature, independently of the air velocity range. Moreover, critical velocities vary linearly with initial temperature. In addition, attachment and lift-off heights have been obtained from CH* chemiluminescence visualization. Results point out that the attachment height decreases significantly with temperature. Observations also indicate that the intrinsic process of lifting is modified. Pre-lifting anchored flame local extinctions, not observed at room-temperature, appear at higher initial temperatures; their occurrence increases with temperature. The lift-off height of turbulent lifted flames is also reduced with temperature. Overall, results show that increasing local temperature in the stabilization zone enhances flame stability.

scholarly journals Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

2012 ◽  
Vol 22 (2) ◽  
pp. 401-408 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Andrzej Ruszewski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Type Model ◽  
Stability Tests ◽  
Numerical Examples ◽  
Computer Methods ◽  
Discrete Linear Systems ◽  
Complex Functions ◽  
The Stability

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systemsAsymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

scholarly journals Impact of the Nuclear Equation of State on the Stability of Hybrid Neutron Stars

Universe ◽  
2019 ◽  
Vol 5 (8) ◽  
pp. 186 ◽  
Author(s):  
Mateusz Cierniak ◽  
Tobias Fischer ◽  
Niels-Uwe Bastian ◽  
Thomas Klähn ◽  
Marc Salinas
Keyword(s):  
Equations Of State ◽  
Mean Field Theory ◽  
Mean Field ◽  
Type Model ◽  
Two Phase ◽  
Relativistic Mean Field ◽  
Nuclear Equation Of State ◽  
Hot Matter ◽  
The Stability ◽  
Quark Phase

We construct a set of equations of state (EoS) of dense and hot matter with a 1st order phase transition from a hadronic system to a deconfined quark matter state. In this two-phase approach, hadrons are described using the relativistic mean field theory with different parametrisations and the deconfined quark phase is modeled using vBag, a bag–type model extended to include vector interactions as well as a simultaneous onset of chiral symmetry restoration and deconfinement. This feature results in a non–trivial connection between the hadron and quark EoS, modifying the quark phase beyond its onset density. We find that this unique property has an impact on the predicted hybrid (quark core) neutron star mass–radius relations.

scholarly journals Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu ◽  
Imtiaz Ahmad
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Models ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Compact Finite Difference Method ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
The Stability

Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.

scholarly journals Stellar scattering and the formation of exponential discs in self-gravitating systems

2020 ◽  
Vol 499 (2) ◽  
pp. 2672-2684
Author(s):  
Jian Wu ◽  
Curtis Struck ◽  
Elena D’Onghia ◽  
Bruce G Elmegreen
Keyword(s):  
Velocity Dispersion ◽  
Stellar Orbits ◽  
Poisson Equations ◽  
Abrupt Changes ◽  
Gradient Solution ◽  
Stellar Velocity ◽  
Zero Entropy ◽  
Profile Changes ◽  
The Stability ◽  
Gravitating Systems

ABSTRACT We show, using the N-body code gadget-2, that stellar scattering by massive clumps can produce exponential discs, and the effectiveness of the process depends on the mass of scattering centres, as well as the stability of the galactic disc. Heavy, dense scattering centres in a less stable disc generate an exponential profile quickly, with a time-scale shorter than 1 Gyr. The profile evolution due to scattering can make a near-exponential disc under various initial stellar distributions. This result supports analytic theories that predict the scattering processes always favour the zero entropy gradient solution to the Jeans/Poisson equations, whose profile is a near-exponential. Profile changes are accompanied by disc thickening, and a power-law increase in stellar velocity dispersion in both vertical and radial directions is also observed through the evolution. Close encounters between stars and clumps can produce abrupt changes in stellar orbits and shift stars radially. These events can make trajectories more eccentric, but many leave eccentricities little changed. On average, orbital eccentricities of stars increase moderately with time.

scholarly journals Chaos in a Tumor Growth Model with Delayed Responses of the Immune System

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. Saleem ◽  
Tanuja Agrawal
Keyword(s):  
Immune System ◽  
Time Delay ◽  
Present Model ◽  
Type Model ◽  
Tumor Growth Model ◽  
Discrete Time Delay ◽  
Delay Effects ◽  
Equilibrium Level ◽  
The Stability ◽  
Growth Of Tumor

A simple prey-predator-type model for the growth of tumor with discrete time delay in the immune system is considered. It is assumed that the resting and hunting cells make the immune system. The present model modifies the model of El-Gohary (2008) in that it allows delay effects in the growth process of the hunting cells. Qualitative and numerical analyses for the stability of equilibriums of the model are presented. Length of the time delay that preserves stability is given. It is found that small delays guarantee stability at the equilibrium level (stable focus) but the delays greater than a critical value may produce periodic solutions through Hopf bifurcation and larger delays may even lead to chaotic attractors. Implications of these results are discussed.

APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350055 ◽  
Author(s):  
SHYAN-SHIOU CHEN ◽  
CHANG-YUAN CHENG ◽  
YI-RU LIN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Type Model ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Trapping Region ◽  
Saddle Node ◽  
The Stability ◽  
Two Equilibria

In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh–Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: (1) the number and stability of the equilibria are analyzed in detail using a table to demonstrate the matter in which the stability of the equilibrium changes and to determine which two equilibria collapse through the saddle-node bifurcation; (2) the sufficient conditions for an Andronov–Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and (3) we elaborately evaluate the sufficient conditions for the Bogdanov–Takens (BT) and Bautin bifurcations. Several numerical simulations for these conditions are also presented. In particular, two types of bistable behaviors are numerically demonstrated: the BT and Bautin bifurcations. Notably, all of the bifurcation curves in the domain of the remaining parameters are similar when the time scale is large. Additionally, to show the potential for a limit cycle, the existence of a trapping region is demonstrated. These results present a variety of diverse behaviors for this model. The results of this study will be helpful in assessing suitable parameters for fitting the resemblances of experimental observations.

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