scholarly journals Spatial heterogeneity enhance robustness of large multi-species ecosystems

2021 ◽  
Author(s):  
Susanne Marie Pettersson ◽  
Martin Nilsson Jacobi
Keyword(s):  
Spatial Heterogeneity ◽  
Heterogeneous Systems ◽  
Ecosystem Dynamics ◽  
Volterra Model ◽  
Remarkable Change ◽  
Stability Boundaries ◽  
Stability Change ◽  
Spatial Environment ◽  
Species Abundances ◽  
The Stability

Understanding ecosystem stability and functioning is a long-standing goal in theoretical ecology, with one of the main tools being dynamical modelling of species abundances. With the help of dynamical population models limits to stability and regions of various ecosystem dynamics have been extensively mapped in terms of diversity (number of species), types of interactions, interaction strengths, varying interaction networks (for example plant-pollinator, food-web) and varying structures of these networks. Although it is apparent that ecosystems reside in and are affected by a spatial environment, local differences (spatial heterogeneity) is often excluded from studies mapping stability boundaries under the assumption of an average and equal amount of interaction for all individuals of a species. Here we show that extending the classic dynamical Generalised-Lotka-Volterra model into a connected space the boundaries of stability change. When viewing the ecosystem as a spatially heterogeneous whole, limits previously marking the end of stability can now be crossed without any remarkable change in species abundances and without loss of stability. Thus limits previously thought to mark catastrophic transitions are not critical due to the possibility of spatial heterogeneity within the system. In addition, we show that too much spatial fragmentation of ecosystem habitats acts destabilising and leads back to the stability boundaries found in spatially homogeneous ecosystems with average interactions. Thus, we conclude that spatially heterogeneous but connected systems are the most robust. In terms of ecosystem management, the risk of collapse or irreversible changes is lower in spatially heterogeneous systems, which real ecosystems are, and we should expect local changes in populations well in advance of system collapse. Although, too much fragmentation of an ecosystem's available space can lead to a less robust system with higher risk of extinctions and collapse.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

Host-Guest Interactions on Electrode Surfaces for Immobilization of Molecular Catalysts

2020 ◽  
Author(s):  
Laurent Sévery ◽  
Jacek Szczerbiński ◽  
Mert Taskin ◽  
Isik Tuncay ◽  
Fernanda Brandalise Nunes ◽  
...  
Keyword(s):  
Aqueous Media ◽  
Heterogeneous Systems ◽  
Catalytic Systems ◽  
New Approach ◽  
Molecular Systems ◽  
Electrode Surfaces ◽  
Catalytic Surfaces ◽  
Oxide Electrodes ◽  
The Stability ◽  
Molecular Catalysts

The strategy of anchoring molecular catalysts on electrode surfaces combines the high selectivity and activity of molecular systems with the practicality of heterogeneous systems. The stability of molecular catalysts is, however, far less than that of traditional heterogeneous electrocatalysts, and therefore a method to easily replace anchored molecular catalysts that have degraded could make such electrosynthetic systems more attractive. Here, we apply a non-covalent “click” chemistry approach to reversibly bind molecular electrocatalysts to electrode surfaces via host-guest complexation with surface-anchored cyclodextrins. The host-guest interaction is remarkably strong and allows the flow of electrons between the electrode and the guest catalyst. Electrosynthesis in both organic and aqueous media was demonstrated on metal oxide electrodes, with stability on the order of hours. The catalytic surfaces can be recycled by controlled release of the guest from the host cavities and readsorption of fresh guest. This strategy represents a new approach to practical molecular-based catalytic systems.

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

scholarly journals Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Qiu ◽  
Wenmin Deng ◽  
Mingqi Xiang
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Optimal Harvesting ◽  
Ergodic Method ◽  
Technical Assumption ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
The Stability ◽  
Lévy Jumps

AbstractThe aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

scholarly journals Cellular ATP Levels Determine the Stability of a Nucleotide Kinase

2021 ◽  
Vol 8 ◽  
Author(s):  
Oliver Brylski ◽  
Puja Shrestha ◽  
Patricia Gnutt ◽  
David Gnutt ◽  
Jonathan Wolf Mueller ◽  
...  
Keyword(s):  
Protein Stability ◽  
Bound States ◽  
Atp Depletion ◽  
Aps Kinase ◽  
Cellular Processes ◽  
Atp Levels ◽  
Stability Change ◽  
Cell Stability ◽  
The Stability ◽  
Nucleotide Kinase

The energy currency of the cell ATP, is used by kinases to drive key cellular processes. However, the connection of cellular ATP abundance and protein stability is still under investigation. Using Fast Relaxation Imaging paired with alanine scanning and ATP depletion experiments, we study the nucleotide kinase (APSK) domain of 3′-phosphoadenosine-5′-phosphosulfate (PAPS) synthase, a marginally stable protein. Here, we show that the in-cell stability of the APSK is determined by ligand binding and directly connected to cellular ATP levels. The observed protein stability change for different ligand-bound states or under ATP-depleted conditions ranges from ΔGf0 = -10.7 to +13.8 kJ/mol, which is remarkable since it exceeds changes measured previously, for example upon osmotic pressure, cellular stress or differentiation. The results have implications for protein stability during the catalytic cycle of APS kinase and suggest that the cellular ATP level functions as a global regulator of kinase activity.

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.

Influence of Gravity and Taper on the Vibration of a Standing Column

2012 ◽  
Vol 4 (04) ◽  
pp. 483-495 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Cross Section ◽  
Numerical Stability ◽  
Natural Vibration ◽  
Vibration Frequencies ◽  
Stability Criteria ◽  
Initial Value ◽  
Vertical Column ◽  
Stability Boundaries ◽  
Section Shape ◽  
The Stability

AbstractThe stability and natural vibration of a standing tapered vertical column under its own weight are studied. Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column. For vibrations we use an accurate, efficient initial value numerical method for the first three frequencies. Four kinds of columns with linear taper are considered. Both the taper and the cross section shape of the column have large influences on the vibration frequencies. It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency. Vibrations may occur in two different planes.

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