scholarly journals Tipping point and noise-induced transients in ecological networks

2020 ◽  
Vol 17 (171) ◽  
pp. 20200645
Author(s):  
Yu Meng ◽  
Ying-Cheng Lai ◽  
Celso Grebogi
Keyword(s):  
Steady State ◽  
Scaling Laws ◽  
First Passage Time ◽  
Gaussian White Noise ◽  
Tipping Point ◽  
High Dimensional ◽  
Stable Steady State ◽  
Dynamical Mechanism ◽  
Mutualistic Networks ◽  
Demographic Noise

A challenging and outstanding problem in interdisciplinary research is to understand the interplay between transients and stochasticity in high-dimensional dynamical systems. Focusing on the tipping-point dynamics in complex mutualistic networks in ecology constructed from empirical data, we investigate the phenomena of noise-induced collapse and noise-induced recovery. Two types of noise are studied: environmental (Gaussian white) noise and state-dependent demographic noise. The dynamical mechanism responsible for both phenomena is a transition from one stable steady state to another driven by stochastic forcing, mediated by an unstable steady state. Exploiting a generic and effective two-dimensional reduced model for real-world mutualistic networks, we find that the average transient lifetime scales algebraically with the noise amplitude, for both environmental and demographic noise. We develop a physical understanding of the scaling laws through an analysis of the mean first passage time from one steady state to another. The phenomena of noise-induced collapse and recovery and the associated scaling laws have implications for managing high-dimensional ecological systems.

scholarly journals Predicting tipping points in mutualistic networks through dimension reduction

2018 ◽  
Vol 115 (4) ◽  
pp. E639-E647 ◽  
Author(s):  
Junjie Jiang ◽  
Zi-Gang Huang ◽  
Thomas P. Seager ◽  
Wei Lin ◽  
Celso Grebogi ◽  
...  
Keyword(s):  
Dimension Reduction ◽  
Reduction Process ◽  
Real Data ◽  
Tipping Point ◽  
Networked Systems ◽  
Weighted Averaging ◽  
Dynamical Mechanism ◽  
Point Of No Return ◽  
2D System ◽  
Mutualistic Networks

Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a “point of no return”) at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.

scholarly journals Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP

2012 ◽  
Vol 6 (3) ◽  
pp. 573-588 ◽  
Author(s):  
F. Pattyn ◽  
C. Schoof ◽  
L. Perichon ◽  
R. C. A. Hindmarsh ◽  
E. Bueler ◽  
...  
Keyword(s):  
Steady State ◽  
Adaptive Mesh Refinement ◽  
Ice Sheet ◽  
Adaptive Mesh ◽  
Stable Steady State ◽  
Fixed Grid ◽  
Approximate Analytical Solutions ◽  
Grounding Line ◽  
Intercomparison Project ◽  
Line Positions

Abstract. Predictions of marine ice-sheet behaviour require models that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise for marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no effects of lateral buttressing). Unique steady state grounding line positions exist for ice sheets on a downward sloping bed, while hysteresis occurs across an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections. Models based on the shallow ice approximation, which does not resolve extensional stresses, do not reproduce the approximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving "shelfy stream" models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid models that generally perform poorly at coarse resolution. Fixed grid models, with nested grid representations of the grounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients.

Transient behavior of regulated Brownian motion, I: Starting at the origin

1987 ◽  
Vol 19 (03) ◽  
pp. 560-598 ◽  
Author(s):  
Joseph Abate ◽  
Ward Whitt
Keyword(s):  
Brownian Motion ◽  
Steady State ◽  
First Passage Time ◽  
Cumulative Distribution ◽  
Stochastic Flow ◽  
Completely Monotone ◽  
Constant Diffusion ◽  
Flow Systems ◽  
The Moment ◽  
First Moment

A natural model for stochastic flow systems is regulated or reflecting Brownian motion (RBM), which is Brownian motion on the positive real line with constant negative drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at the origin. As a basis for understanding how stochastic flow systems approach steady state, this paper provides relatively simple descriptions of the moments of RBM as functions of time. In Part I attention is restricted to the case in which RBM starts at the origin; then the moment functions are increasing. After normalization by the steady-state limits, these moment c.d.f.&s (cumulative distribution functions) coincide with gamma mixtures of inverse Gaussian c.d.f.&s. The first moment c.d.f. thus coincides with the first-passage time to the origin starting in steady state with the exponential stationary distribution. From this probabilistic characterization, it follows that thekth-moment c.d.f is thek-fold convolution of the first-moment c.d.f. As a consequence, it is easy to see that the (k +1)th moment approaches its steady-state limit more slowly than thekthmoment. It is also easy to derive the asymptotic behavior ast→∞. The first two moment c.d.f.&s have completely monotone densities, supporting approximation by hyperexponential (H2)c.d.f.&s (mixtures of two exponentials). TheH2approximations provide easily comprehensible descriptions of the first two moment c.d.f.&s suitable for practical purposes. The two exponential components of theH2approximation yield simple exponential approximations in different regimes. On the other hand, numerical comparisons show that the limit related to the relaxation time does not predict the approach to steady state especially well in regions of primary interest. In Part II (Abate and Whitt (1987a)), moments of RBM with non-zero initial conditions are treated by representing them as the difference of two increasing functions, one of which is the moment function starting at the origin studied here.

scholarly journals Suppression of marine ice sheet instability

2018 ◽  
Vol 857 ◽  
pp. 648-680 ◽  
Author(s):  
Samuel S. Pegler
Keyword(s):  
Steady State ◽  
Rapid Assessment ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Stable Steady State ◽  
Ice Shelf ◽  
West Antarctic Ice Sheet ◽  
West Antarctic ◽  
Grounding Line ◽  
The Stability

A long-standing open question in glaciology concerns the propensity for ice sheets that lie predominantly submerged in the ocean (marine ice sheets) to destabilise under buoyancy. This paper addresses the processes by which a buoyancy-driven mechanism for the retreat and ultimate collapse of such ice sheets – the marine ice sheet instability – is suppressed by lateral stresses acting on its floating component (the ice shelf). The key results are to demonstrate the transition between a mode of stable (easily reversible) retreat along a stable steady-state branch created by ice-shelf buttressing to tipped (almost irreversible) retreat across a critical parametric threshold. The conditions for triggering tipped retreat can be controlled by the calving position and other properties of the ice-shelf profile and can be largely independent of basal stress, in contrast to principles established from studies of unbuttressed grounding-line dynamics. The stability and recovery conditions introduced by lateral stresses are analysed by developing a method of constructing grounding-line stability (bifurcation) diagrams, which provide a rapid assessment of the steady-state positions, their natures and the conditions for secondary grounding, giving clear visualisations of global stabilisation conditions. A further result is to reveal the possibility of a third structural component of a marine ice sheet that lies intermediate to the fully grounded and floating components. The region forms an extended grounding area in which the ice sheet lies very close to flotation, and there is no clearly distinguished grounding line. The formation of this region generates an upsurge in buttressing that provides the most feasible mechanism for reversal of a tipped grounding line. The results of this paper provide conceptual insight into the phenomena controlling the stability of the West Antarctic Ice Sheet, the collapse of which has the potential to dominate future contributions to global sea-level rise.

scholarly journals System Approach from Biomass Combustion in Packed Bed Reactor

2007 ◽  
Vol 7 (1 & 2) ◽  
pp. 16 ◽  
Author(s):  
Anhkien Le ◽  
Le Xuan Hai ◽  
V. N. Sharifi ◽  
J. Swithenbank
Keyword(s):  
Steady State ◽  
Transition Period ◽  
Computing Time ◽  
Substrate Inhibition ◽  
Simple Algorithm ◽  
Packed Bed ◽  
Packed Bed Reactor ◽  
Biomass Combustion ◽  
Stable Steady State ◽  
State Tests

A simple algorithm originally proposed by Choong, Paterson and Scott (2002) was tested on a model of an isothermal controlled-cycled stirred tank reactor with substrate inhibition kinetics, (r = 1 ~c). In previous work, this reacting system had been shown to exhibit steady-state multiplicity. The transition period of this system to the stable steady state is sometimes characterized by very slow change followed by a very rapid convergence to the stable steady state. Tests of the Choong-Paterson-Scott algorithm showed that the feature, which prevents premature termination of the calculations prior to reaching the true steady state, is very useful for this system. However, tests of the stopping criterion showed that the other feature of reducing the computing time was not realized in this system.

Heuristic control of bipedal running: steady-state and accelerated

Robotica ◽  
2011 ◽  
Vol 29 (6) ◽  
pp. 939-947
Author(s):  
A. D. Perkins ◽  
K. J. Waldron ◽  
P. J. Csonka
Keyword(s):  
Steady State ◽  
Experimental System ◽  
Legged Robots ◽  
Stable Steady State ◽  
Control Laws ◽  
Mechanical Coupling ◽  
Ankle Joints

SUMMARYThe design, control, and actuation of legged robots that walk is well established, but there remain unsolved problems for legged robots that run. In this work, dynamic principles are used to develop a set of heuristics for controlling bipedal running and acceleration. These heuristics are then converted into control laws for two very different bipedal systems: one with a high-inertia torso and prismatic knees and one with a low-inertia torso, articulated knees, and mechanical coupling between the knee and ankle joints. These control laws are implemented in simulation to achieve stable steady-state running, accelerating, and decelerating. Stable steady-state running is also achieved in a planar experimental system with a semiconstrained torso.

Analysis of chemical kinetic systems over the entire parameter space - I. The Sal’nikov thermokinetic oscillator

1988 ◽  
Vol 416 (1851) ◽  
pp. 391-402 ◽  
Keyword(s):  
Steady State ◽  
Parameter Space ◽  
Limit Cycles ◽  
Stable Limit Cycle ◽  
Chemical Kinetic ◽  
Phase Portraits ◽  
Stable Steady State ◽  
Stable Limit ◽  
Unstable Steady State ◽  
Undamped Oscillations

In this series of papers we re-examine, using recently developed techniques, some chemical kinetic models that have appeared in the literature with a view to obtaining a complete description of all the qualitatively distinct behaviour that the system can exhibit. Each of the schemes is describable by two coupled ordinary differential equations and contain at most three independent parameters. We find that even with these relatively simple chemical schemes there are regions of parameter space in which the systems display behaviour not previously found. Quite often these regions are small and it seems unlikely that they would be found via classical methods. In part I of the series we consider one of the thermally coupled kinetic oscillator models studied by Sal’nikov. He showed that there is a region in parameter space in which the system would be in a state of undamped oscillations because the relevant phase portrait consists of an unstable steady state surrounded by a stable limit cycle. Our analysis has revealed two further regions in which the phase portraits contain, respectively, two limit cycles of opposite stability enclosing a stable steady state and three limit cycles of alternating stability surrounding an unstable steady state. This latter region is extremely small, so much so that it could be reasonably neglected in any predictions made from the model.

scholarly journals Energy Requirement for Maintenance of Adenylate Energy Charge and Metabolic ATP in Platelets During Starvation

1977 ◽  
Author(s):  
J.W.N. Akkerman ◽  
G. Gorter ◽  
J.J. Sixma
Keyword(s):  
Steady State ◽  
Adenine Nucleotides ◽  
Energy Requirement ◽  
Energy Charge ◽  
Lactate Production ◽  
Stable Steady State ◽  
Adenylate Energy Charge ◽  
Consumption Energy ◽  
Steady State Levels ◽  
Lactate Formation

Energy requirements for maintenance of stable adenylate energy charge (AEC) and metabolic ATP(ATP-m)level were studied in gel filtered platelets at various degrees of starvation. Platelets gel filtered and subsequently incubated during 40 min.at 37°C with 1mM CN- and without glucose consumed their glycogen at a rate of 0.79 ± 0.23(± SD, n=6)/μmol glycosyl residues .min-1 10-11 cells. During this period AEC and ATP-m decreased linearly with time at rates of 5-6.10-3 and 0.75-1.05% of total radioactive adenine nucleotides .min-1.10-11 cells respectively. Addition of 25–1000μM glucose increased lactate production and decreased the fall of AEC and ATP-m proportional to the amounts of glucose added. Glycogenolysis remained active below 100μM glucose but ceased at higher glucose concentrations. From these data ATP-m production from glycogenolysis and glycolysis was calculated and compared with the decrease of steady state levels of AEC and ATP-m. A production of 3μmol ATP-m.min-1.10-11 cells was required to maintain initial AEC and ATP-m level. At lower rates of ATP-m production these values fell without reaching stable steady state levels in a lower range. After 40-50 min variations in AEC and ATP-m ceased and lactate formation stopped leaving the cells in a state of hybernation. Subsequent addition of glucoserestored lactate accumulation, AEC and ATP-m. On the basis of formation and steady state levels of ATP-m its consumption was calculated. A lowering production was not completely met by a lowering consumption. Energy consumption in resting platelets is therefore partly independent from energy production.

Development of a Carbon Nanotube-Based Electromechanical Resonator: Device Modeling

2008 ◽  
Author(s):  
Changhong Ke
Keyword(s):  
Steady State ◽  
Carbon Nanotube ◽  
Parallel Plate ◽  
Force Sensing ◽  
Stable Steady State ◽  
Device Modeling ◽  
Complex Relationship ◽  
Novel Device ◽  
Close Form ◽  
Electromechanical Dynamics

We present an electromechanical analysis of a novel double-sided driven carbon nanotube-based electromechanical resonator. The device comprises a cantilevered carbon nanotube actuated by two parallel-plate electrodes. Close-form analytical solutions capable of predicting the steady-state resonation of the device and its resonant pull-in conditions are derived using an energy-based method. Our close-form formulas clearly reveal the complex relationship among the device geometry, the driving voltages, and the device’s electromechanical dynamics. Our theoretical modeling shows that the stable steady-state spanning range of the resonating cantilever substantially exceeds the previously reported quasi-static pull-in limit for single-sided driven cantilevered nanotube-based NEMS, while the resonant pull-in voltage is only a small fraction of the quasi-static pull-in voltage. The unique behaviors of this novel device are expected to significantly enhance the applications of electromechanical resonators in the fields of signal processing, mass and force sensing, and chemical and molecule detection.

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