Math Biosci
Mediterranean Institute of Oceanography (MIO), Aix-Marseille University, Marseille, Cedex 09 13288, France.
Published: July 2018
Two predator-prey model formulations are studied: the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to a singular perturbation problem. In contradiction to the RM-model, the resource for the prey is modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models the transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle occur. The slow-fast limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small amplitude stable limit cycles exist. The predicted dynamics of the MB-model is in a large part of the parameter space similar to that of the RM-model. However, the fast-slow version of MB-model does not predict a canard explosion phenomenon.
Download full-text PDF |
Source |
---|---|
http://dx.doi.org/10.1016/j.mbs.2018.04.006 | DOI Listing |
Inorg Chem
January 2025
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States.
Previous studies on natural samples of pampaloite (AuSbTe) revealed the crystal structure of a potentially cleavable and/or exfoliable material, while studies on natural and synthetic montbrayite (Sb-containing AuTe) claimed various chemical compositions for this low-symmetry compound. Few investigations of synthetic samples have been reported for both materials, leaving much of their chemical, thermal, and electronic characteristics unknown. Here, we investigate the stability, electronic properties, and synthesis of the gold antimony tellurides AuSbTe and AuSbTe (montbrayite).
View Article and Find Full Text PDFInt J Rehabil Res
January 2025
Clinique la Mitterie, cardiac rehabilitation, Lille, France.
Cardiac rehabilitation (CR) is a cornerstone of heart disease (HD) management, enhancing functional capacity and quality of life. Hybrid cardiac rehabilitation (hCR), combining supervised center-based sessions with synchronous, real-time telerehabilitation at home, offers an alternative to conventional CR to overcome logistical barriers such as facility limitations, distance, and pandemic-related disruptions. This randomized controlled trial evaluated the noninferiority of hCR compared to standard CR in improving functional capacity in patients with chronic heart disease, including those with stable coronary artery disease.
View Article and Find Full Text PDFPLoS One
January 2025
School of Pharmacy, Bandung Institute of Technology, Bandung, Indonesia.
Gastric ulcer is a common disorder of the digestive system. The combination of turmeric and honey is known to treat stomach ulcers. However, curcumin, an active component in turmeric, has limitations, i.
View Article and Find Full Text PDFPhys Chem Chem Phys
January 2025
Guizhou Provincial Key Laboratory of Computing and Network Convergence, School of Information, Guizhou University of Finance and Economics, Guiyang, Guizhou 550025, P. R. China.
Developing superionic conductor (SIC) materials offers a promising pathway to achieving high ionic conductivity in solid-state electrolytes (SSEs). The LiGePS (LGPS) family has received significant attention due to its remarkable ionic conductivity among various SIC materials. molecular dynamics (AIMD) simulations have been extensively used to explore the diffusion behavior of Li ions in LiGePS.
View Article and Find Full Text PDFMol Divers
January 2025
Department of Biosciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia.
Dengue is one of the most prevalent viruses transmitted by the Aedes aegypti mosquitoes. Currently, no specific medication is available to treat dengue diseases. The NS2B-NS3 protease is vital during post-translational processing, which is a key target in this study.
View Article and Find Full Text PDFEnter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!
© LitMetric 2025. All rights reserved.