scholarly journals Predicting Collapse of Complex Ecological Systems: Quantifying the Stability-Complexity Continuum

2019 ◽  
Author(s):  
Susanne Pettersson ◽  
Van M. Savage ◽  
Martin Nilsson Jacobi
Keyword(s):  
Single Species ◽  
Ecological Systems ◽  
Ecological Research ◽  
Stability Criteria ◽  
Numerical Techniques ◽  
Intermediate Regime ◽  
Limits Of Stability ◽  
Species Abundances ◽  
The Stability ◽  
Degree Of Instability

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the Extinction Continuum. We also develop a metric that locates the position of the system within the Extinction Continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

scholarly journals Predicting collapse of complex ecological systems: quantifying the stability–complexity continuum

2020 ◽  
Vol 17 (166) ◽  
pp. 20190391 ◽  
Author(s):  
Susanne Pettersson ◽  
Van M. Savage ◽  
Martin Nilsson Jacobi
Keyword(s):  
Single Species ◽  
Ecological Systems ◽  
Ecological Research ◽  
Stability Criteria ◽  
Numerical Techniques ◽  
Intermediate Regime ◽  
Limits Of Stability ◽  
Species Abundances ◽  
The Stability ◽  
Degree Of Instability

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the extinction continuum. We also develop a metric that locates the position of the system within the extinction continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system's behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

scholarly journals A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

2012 ◽  
Vol 1 ◽  
pp. 21-32
Author(s):  
A.V. Papa Rao ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Single Species ◽  
Analytical Investigation ◽  
Optimal Harvesting ◽  
Stability Criteria ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Analytical Stability ◽  
The Stability

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

A SINGLE SPECIES POPULATION IN A POLLUTED ENVIRONMENT

2010 ◽  
Vol 03 (02) ◽  
pp. 187-204 ◽  
Author(s):  
A. K. PAL ◽  
G. P. SAMANTA
Keyword(s):  
Dynamical Behavior ◽  
Single Species ◽  
Ecological Systems ◽  
Point Of View ◽  
Experimental Point ◽  
Discrete Delay ◽  
Environmental Toxicant ◽  
Species Population ◽  
The Stability ◽  
Single Species Population

The effect of toxicants on ecological systems is an important and urgent issue from mathematical and experimental point of view. In this paper, we have studied the dynamical behavior of a single species population affected by environmental toxicant and population toxicant. Boundedness, local and global stabilities, bifurcation are addressed. We have also studied the effect of discrete delay of the environmental toxicant on the instantaneous growth rates of the population biomass and population toxicant due to incubation period. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals On the Destabilizing Effect of Damping in Nonconservative Elastic Systems

1965 ◽  
Vol 32 (3) ◽  
pp. 592-597 ◽  
Author(s):  
G. Herrmann ◽  
Ing-Chang Jong
Keyword(s):  
Critical Load ◽  
Characteristic Equation ◽  
Elastic System ◽  
Viscous Damping ◽  
Stability Criteria ◽  
Elastic Systems ◽  
The Stability ◽  
Proper Interpretation ◽  
Degree Of Instability

The destabilizing effect of linear viscous damping in a nonconservative elastic system is investigated by studying the roots of the characteristic equation in addition to the stability criteria and by introducing the concept of degree of instability. A generic relationship between critical loadings for no damping and for slight damping as well as vanishing damping is established. It is found that while the presence of small damping may have a destabilizing effect, proper interpretation of the limiting process of vanishing damping leads to the same critical load as for no damping.

scholarly journals Continuous integration in urban social-ecological systems science needs to allow for spacing co-existence

AMBIO ◽  
2021 ◽  
Author(s):  
Dagmar Haase
Keyword(s):  
Urban Sustainability ◽  
Ecological Systems ◽  
Urban Systems ◽  
Systems Science ◽  
Ecological Research ◽  
Mutual Relationship ◽  
Continuous Integration ◽  
Social Ecological Systems ◽  
Social Ecological ◽  
Interdisciplinary Journal

AbstractUrbanization brings benefits and burdens to both humans and nature. Cities are key systems for integrated social-ecological research and the interdisciplinary journal of Ambio has published ground-breaking contributions in this field. This reflection piece identifies and discusses integration of the human and natural spheres in urban social-ecological research using the following foundational papers as important milestones: Folke et al. (1997), Ernstson et al. (2010) and Andersson et al. (2014). These papers each take unique approaches that aim to uncover core properties—processes, structures, and actors—of urban systems and set them into mutual relationship. This piece will end with a forward-looking vision for the coming 50 years of urban sustainability and resilience study in Ambio.

Dissipative instability of the MHD tangential discontinuity in magnetized plasmas with anisotropic viscosity and thermal conductivity

1996 ◽  
Vol 56 (2) ◽  
pp. 285-306 ◽  
Author(s):  
M. S. Ruderman ◽  
E. Verwichte ◽  
R. Erdélyi ◽  
M. Goossens
Keyword(s):  
Thermal Conductivity ◽  
Dispersion Equation ◽  
Viscosity Coefficient ◽  
Tangential Discontinuity ◽  
Stability Criteria ◽  
Threshold Velocity ◽  
Cold Plasmas ◽  
The Difference ◽  
The Stability ◽  
Anisotropic Viscosity

The stability of the MHD tangential discontinuity is studied in compressible plasmas in the presence of anisotropic viscosity and thermal conductivity. The general dispersion equation is derived, and solutions to this dispersion equation and stability criteria are obtained for the limiting cases of incompressible and cold plasmas. In these two limiting cases the effect of thermal conductivity vanishes, and the solutions are only influenced by viscosity. The stability criteria for viscous plasmas are compared with those for ideal plasmas, where stability is determined by the Kelvin—Helmholtz velocity VKH as a threshold for the difference in the equilibrium velocities. Viscosity turns out to have a destabilizing influence when the viscosity coefficient takes different values at the two sides of the discontinuity. Viscosity lowers the threshold velocity V below the ideal Kelvin—Helmholtz velocity VKH, so that there is a range of velocities between V and VKH where the overstability is of a dissipative nature.

Intrinsic Thermal Stability of Anisotropic Thin-Film Superconductors

1990 ◽  
Vol 112 (1) ◽  
pp. 10-15 ◽  
Author(s):  
M. I. Flik ◽  
C. L. Tien
Keyword(s):  
Thin Film ◽  
Thermal Stability ◽  
Stability Criterion ◽  
High Temperature Superconductors ◽  
Stability Criteria ◽  
Anisotropic Thermal Conductivity ◽  
Operating Current ◽  
Released Energy ◽  
The Stability ◽  
Thermal Stability Of

Intrinsic thermal stability denotes a situation where a superconductor can carry the operating current without resistance at all times after the occurrence of a localized release of thermal energy. This novel stability criterion is different from the cryogenic stability criteria for magnets and has particular relevance to thin-film superconductors. Crystals of ceramic high-temperature superconductors are likely to exhibit anisotropic thermal conductivity. The resultant anisotropy of highly oriented films of superconductors greatly influences their thermal stability. This work presents an analysis for the maximum operating current density that ensures intrinsic stability. The stability criterion depends on the amount of released energy, the Biot number, the aspect ratio, and the ratio of the thermal conductivities in the plane of the film and normal to it.

scholarly journals The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

scholarly journals First year of the new Arctic AWIPEV-COSYNA cabled Underwater Observatory in Kongsfjorden, Spitsbergen

2016 ◽  
Author(s):  
Philipp Fischer ◽  
Max Schwanitz ◽  
Reiner Loth ◽  
Uwe Posner ◽  
Markus Brand ◽  
...  
Keyword(s):  
Statistical Power ◽  
Single Species ◽  
First Year ◽  
Total Abundance ◽  
Digital Sampling ◽  
Scientific Analysis ◽  
Data Density ◽  
Species Abundances ◽  
Sampling Procedures ◽  
Total Species

Abstract. A combined year round assessment of selected oceanographic data and a macrobiotic community assessment was performed from October 2013 to November 2014 in the littoral zone of the polar fjord systems Kongsfjorden on the west coast of Svalbard (Norway). A state of the art remote controlled cabled underwater observatory technology was used for daily vertical profiles of temperature, salinity and turbidity together with a stereo-optical assessment of the macrobiotic community, including fish. The results reveal a distinct seasonal cycle in total species abundances with a significantly higher total abundance and species richness during the polar winter when no light is available under water compared to the summer months when 24-h light is available. During the winter months, a temporally highly segmented community was observed with respect to species occurrence with single species dominating the winter community for restricted times. In contrast, the summer community showed an overall lower total abundance, as well as a significantly lower number of species. The study clearly demonstrates the high potential of cable connected remote controlled digital sampling devices, especially in remote areas, such as the polar fjord systems, with harsh environmental conditions and limited accessibility. A smart combination of such new digital “sampling” methods with classic sampling procedures can provide a possibility to significantly extend the sampling time and frequency especially in remote and difficult to access areas. This can help to provide a sufficient data density and therefore statistical power for a sound scientific analysis without increasing the invasive sampling pressure in ecologically sensitive environments.

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