An exact solution of a diffusive predator–prey system

2005 ◽  
Vol 461 (2056) ◽  
pp. 1029-1053 ◽  
Author(s):  
Sergei Petrovskii ◽  
Horst Malchow ◽  
Bai-Lian Li
Keyword(s):  
Exact Solution ◽  
Large Time ◽  
Temporal Dynamics ◽  
Nonlinear Partial Differential Equations ◽  
Predator Prey ◽  
Change Of Variables ◽  
Spatio Temporal ◽  
Parameter Values ◽  
The Impact ◽  
Large Time Limit

We consider a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator–prey community where the prey per capita growth rate is damped by the Allee effect. Using an appropriate change of variables, we obtain an exact solution of the system, which appears to be related to the issue of biological invasion. In the large-time limit, or for appropriate parameter values, this solution describes the propagation of a travelling population front. We show that the properties of the solution exhibit biologically reasonable dependence on the parameter values; in particular, it predicts that the travelling front of invasive species can be stopped or reversed owing to the impact of predation.

scholarly journals Spatio-temporal dynamics of schistosomiasis in Rwanda between 2001 and 2012: impact of the national Neglected Tropical Disease control programme

2017 ◽  
Vol 12 (1) ◽  
Author(s):  
Elias Nyandwi ◽  
Tom Veldkamp ◽  
Frank Badu Osei ◽  
Sherif Amer
Keyword(s):  
Temporal Dynamics ◽  
Public Health Problem ◽  
Incidence Rates ◽  
Control Programme ◽  
Scan Statistics ◽  
Major Public Health Problem ◽  
Implementation Phase ◽  
Incidence Data ◽  
Spatio Temporal ◽  
The Impact

Schistosomiasis is recognised as a major public health problem in Rwanda. We aimed to identify the spatio-temporal dynamics of its distribution at a fine-scale spatial resolution and to explore the impact of control programme interventions. Incidence data of Schistosoma mansoni infection at 367 health facilities were obtained for the period 2001-2012. Disease cluster analyses were conducted using spatial scan statistics and geographic information systems. The impact of control interventions was assessed for three distinct sub-periods. Findings demonstrated persisting, emerging and re-emerging clusters of schistosomiasis infection across space and time. The control programme initially caused an abrupt increase in incidence rates during its implementation phase. However, this was followed by declining and disappearing clusters when the programme was fully in place. The findings presented should contribute to a better understanding of the dynamics of schistosomiasis distribution to be used when implementing future control activities, including prevention and elimination efforts.

Predicting change in biogeochemical potential of subsurface systems with changing hydrogeological conditions

2021 ◽  
Author(s):  
Swamini Khurana ◽  
Falk Heße ◽  
Martin Thullner
Keyword(s):  
Water Quality ◽  
Preferential Flow ◽  
Nutrient Loading ◽  
Temporal Dynamics ◽  
Reaction Network ◽  
Climate Scenario ◽  
Ecosystem Functions ◽  
External Forcing ◽  
Spatio Temporal ◽  
The Impact

<p>In a changing climate scenario, we expect weather event patterns to change, both in frequency and in intensity. The subsequent impacts of these changing patterns on ecosystem functions are of great interest. Water quality particularly is critical due to public health concerns. Already, seasonal variation of water quality has been attributed to varying microbial community assemblages and nutrient loading in the corresponding water body but the contribution of the variations in the quantity of groundwater recharge is a missing link. It is thus beneficial to establish links between external forcing such as changing infiltration rate or recharge on nutrient cycling in the subsurface. We undertake this study to investigate the impact of temporal variation in external forcing on the biogeochemical potential of spatially heterogeneous subsurface systems using a numerical modeling approach. We used geostatistical tools to generate spatial random fields by considering difference combinations of the variance in the log conductivity field and the anisotropy of the domain. Tuning these two parameters assists in effective representation of a wide variety of geologic materials with varying intensity of preferential flow paths in the heterogeneous domain. We ran simulations using OGS#BRNS that enables us to combine a flexibly defined microbial mediated reaction network with the mentioned spatially heterogeneous domains in transient conditions. We propose that a combination of estimated field indicators of Damköhler number, Peclet number (transformed Damköhler number: Da<sub>t</sub>), and projected temporal dynamics in surface conditions can assist us in predicting the change in biogeochemical potential of the subsurface system. Preliminary results indicate that we miss potentially critical variations in reactive species concentration if we neglect spatio-temporal heterogeneities for regimes where 1<Da<sub>t</sub><40. For regimes characterized by values outside this range, we propose that spatio-temporal heterogeneities due to subsurface structure and changing hydrological forcing may not be relevant.</p>

DIFFUSION-DRIVEN INSTABILITIES AND SPATIO-TEMPORAL PATTERNS IN AN AQUATIC PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS TYPE FUNCTIONAL RESPONSE

2011 ◽  
Vol 21 (03) ◽  
pp. 663-684 ◽  
Author(s):  
RANJIT KUMAR UPADHYAY ◽  
N. K. THAKUR ◽  
V. RAI
Keyword(s):  
Pattern Formation ◽  
Spatial Heterogeneity ◽  
Collective Motion ◽  
Temporal Dynamics ◽  
Fish Predation ◽  
Building Blocks ◽  
Aquatic System ◽  
Predator Species ◽  
Predator Prey ◽  
Spatio Temporal

Predator–prey communities are building blocks of an ecosystem. Feeding rates reflect interference between predators in several situations, e.g. when predators form a dense colony or perform collective motion in a school, encounter prey in a region of limited size, etc. We perform spatio-temporal dynamics and pattern formation in a model aquatic system in both homogeneous and heterogeneous environments. Zooplanktons are predated by fishes and interfere with individuals of their own community. Numerical simulations are carried out to explore Turing and non-Turing spatial patterns. We also examine the effect of spatial heterogeneity on the spatio-temporal dynamics of the phytoplankton–zooplankton system. The phytoplankton specific growth rate is assumed to be a linear function of the depth of the water body. It is found that the spatio-temporal dynamics of an aquatic system is governed by three important factors: (i) intensity of interference between the zooplankton, (ii) rate of fish predation and (iii) the spatial heterogeneity. In an homogeneous environment, the temporal dynamics of prey and predator species are drastically different. While prey species density evolves chaotically, predator densities execute a regular motion irrespective of the intensity of fish predation. When the spatial heterogeneity is included, the two species oscillate in unison. It has been found that the instability observed in the model aquatic system is diffusion driven and fish predation acts as a regularizing factor. We also observed that spatial heterogeneity stabilizes the system. The idea contained in the paper provides a better understanding of the pattern formation in aquatic systems.

scholarly journals Regional Public Stock Reductions in Spain: Estimations from a Multiregional Spatial Vector Autorregressive Model

REGION ◽  
2017 ◽  
Vol 4 (1) ◽  
pp. 129 ◽  
Author(s):  
Miguel A Márquez ◽  
Julian Ramajo ◽  
Geoffrey Hewings
Keyword(s):  
Economic Growth ◽  
Temporal Dynamics ◽  
Public Investment ◽  
Public Capital ◽  
Regional Economic Growth ◽  
State Variables ◽  
Regional System ◽  
Negative Effect ◽  
Spatio Temporal ◽  
The Impact

The estimation of the impact of public investment on regional economic growth requires consideration of the spatio-temporal dynamics among the state variables of each region.  Recent austerity policies in Spain that feature temporary decreases in the accumulation of regional public capital should thus be evaluated in terms of their impact on the economy as a whole, on specific regions together with the spillovers effects from one region to the rest of the regional system.  Applying a multiregional integrated specification to model interdependencies across regions, our results indicate that, while global decreases in public investment have a homogenously negative effect on the output of all the regions, the Spanish regions portray heterogeneous responses from localized public capital stock reductions over the simulation period considered.

Spatio-Temporal Dynamics of Sociology in Post-1990 Turkey

2019 ◽  
Vol 24 (4) ◽  
pp. 598-616
Author(s):  
Canan Neşe Kınıkoğlu
Keyword(s):  
Temporal Dynamics ◽  
Sociological Research ◽  
Sociological Knowledge ◽  
Social Foundations ◽  
Methodological Nationalism ◽  
Turkish Nationalism ◽  
Spatial Differences ◽  
Phd Theses ◽  
Spatio Temporal ◽  
The Impact

This study explores the spatio-temporal conditions of producing sociological knowledge at universities at a time of transformation in post-1990 (1990–2017) Turkey. Through a content analysis of the sociology PhD theses submitted in this period, it investigates the questions of where, when, and how sociological knowledge is institutionalized in Turkey. The study has two main findings. First, spatial distribution of sociology PhD theses highlights the ensuing centre–periphery relationships inside Turkey, a country itself located in the periphery. Endowed with better resources, the centre (mainly Ankara and Istanbul) focuses on macro solutions to the problems faced by Turkey and other countries, whereas the rest of the country produces knowledge about their immediate surroundings, that is, particular regions/cities/towns of Turkey. This difference illustrates the degrees to which sociological research in post-1990 Turkey is territorially limited by (Turkish) national borders. Second, temporally speaking, the sociological interest in domestic issues revolves mainly around ‘politics’ and ‘economy’, insofar as they relate to the economic crises, neoliberalism, globalization, and democratization attempts Turkey experienced in the post-1990 period. A closer reading of this spatio-temporality may suggest that Turkish sociology is susceptible to methodological nationalism that downplays the impact of nationalism, conforms to the nation-state and nations, and territorially limits the unit of analysis. Despite the transformations brought about by the period and the spatial differences in knowledge production between the centre and the periphery, sociology in Turkey is bound by the national territorial and ideational boundaries, reproducing the ethnic, political, cultural, and social foundations of Turkish nationalism. This study argues that although Turkish sociology stands on the periphery within the non-Western context, it is nonetheless formalized around its own centre–periphery relationship within the country itself, and that its spatio-temporal institutionalization in the post-1990 period has reproduced an implicit methodological nationalism that relies on Turkish nationalism.

scholarly journals Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics

2020 ◽  
Vol 378 (2173) ◽  
pp. 20190388 ◽  
Author(s):  
Matthew J. Hoffman ◽  
Elizabeth M. Cherry
Keyword(s):  
Data Assimilation ◽  
Temporal Dynamics ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Model Error ◽  
Model Parameters ◽  
Ensemble Spread ◽  
Spatio Temporal ◽  
System States ◽  
Parameter Values

Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm’s sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.

scholarly journals A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

2012 ◽  
Vol 22 (2) ◽  
pp. 313-326 ◽  
Author(s):  
Ewaryst Rafajłowicz ◽  
Krystyn Styczeń ◽  
Wojciech Rafajłowicz
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Temporal Dynamics ◽  
Nonlinear Partial Differential Equations ◽  
Filter Method ◽  
Sqp Method ◽  
Spatio Temporal ◽  
Filter Approach

A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamicsOur aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.

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