scholarly journals Study of internal oscillations in a dynamic system through an external signal implemented in circadian rhythms

2021 ◽  
Vol 2073 (1) ◽  
pp. 012007
Author(s):  
F Mesa ◽  
J R González-Granada ◽  
G Correa-Vélez
Keyword(s):  
External Signal ◽  
Physical Analysis ◽  
Stable Limit ◽  
Biological Models ◽  
Numerical Techniques ◽  
Final Development ◽  
System Versus ◽  
Internal Oscillator ◽  
The Moment ◽  
Stable Limit Cycles

Abstract Through the analysis carried out on a dynamic model that is represented as a system of ordinary differential equations that describes the behavior of the circadian cycles; we will show and analyze in the next document what are the conditions that allow the synchronization of the circadian clock oscillator with the external modification oscillator. The implementation of this type of techniques in anatomical problems is highlighted, which are rare in the literature. The implementations will be carried out through different simulations using numerical techniques and the way in which we will determine the coupling conditions of an internal cycle of the system versus external cycles will be detailed. In the final development of this work, we will be able to see in the model without an external modification signal the existence of stable limit cycles and discover the moment in which the synchronization of the internal oscillator and the external modification signal occurs. These types of problems are common when making biological models that are described by a physical analysis.

scholarly journals Operating diagram of a flocculation model in the chemostat

2020 ◽  
Vol Volume 31 - 2019 - CARI 2018 ◽  
Author(s):  
Radhouane Fekih-Salem ◽  
Tewfik Sari
Keyword(s):  
Local Stability ◽  
Stability Region ◽  
Steady States ◽  
Complete Analysis ◽  
Stable Limit ◽  
Control Parameters ◽  
Coexistence Region ◽  
Microbial Ecosystem ◽  
International Audience ◽  
Stable Limit Cycles

International audience The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species. L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. Le modèle pré-sente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables. De plus, nous déterminons le diagramme opératoire qui dé-crit le comportement asymptotique du système par rapport aux paramètres de contrôle. Il montre l'émergence d'une région de bi-stabilité via une bifurcation noeud col et l'occurrence d'une région de coexistence via une bifurcation transcritique. Enfin, nous illustrons l'importance de la mortalité sur la déstabilisation de l'écosystème microbien en favorisant le lessivage des espèces.

Response : Stable Limit Cycles in Prey-Predator Populations

Science ◽  
1973 ◽  
Vol 181 (4104) ◽  
pp. 1074-1074
Author(s):  
Robert M. May
Keyword(s):  
Limit Cycles ◽  
Stable Limit ◽  
Stable Limit Cycles

The Nonlinear Behavior of Heavy-Duty Truck Combinations With Respect to Straightline Stability

1989 ◽  
Vol 111 (4) ◽  
pp. 577-582 ◽  
Author(s):  
A. Stribersky ◽  
P. S. Fancher
Keyword(s):  
Nonlinear Stability ◽  
Bifurcation Theory ◽  
Nonlinear Behavior ◽  
Stable Limit ◽  
Heavy Duty ◽  
Stability Boundaries ◽  
Stability Behavior ◽  
Heavy Duty Truck ◽  
Straight Line ◽  
Stable Limit Cycles

A comparison of the nonlinear stability behavior of the steady state straight line motion of truck combinations with and without a second trailer is shown. These investigations have been done by applying bifurcation theory. Stability boundaries in the parameter space and the corresponding bifurcation solutions are given. Depending on the loading conditions, unstable and also stable limit cycles have been found. Particular emphasis is given to the influence of the frictional coupling between tire and road on the nonlinear stability behavior of these vehicles.

On the Bifurcation Structure of a Leslie–Tanner Model with a Generalist Predator

2020 ◽  
Vol 30 (06) ◽  
pp. 2050088
Author(s):  
Luis Miguel Valenzuela ◽  
Gamaliel Blé ◽  
Manuel Falconi
Keyword(s):  
Generalist Predator ◽  
Hopf Bifurcations ◽  
Stable Limit ◽  
Previous Knowledge ◽  
Bifurcation Structure ◽  
Remarkable Feature ◽  
Predator Prey ◽  
Predator Prey Model ◽  
The Subject ◽  
Stable Limit Cycles

In this work, the dynamical properties of a Leslie–Tanner predator–prey model are analyzed. A method is provided to find the regions in the parameter space where Bautin, Hopf and simultaneous supercritical Hopf bifurcations exist. A remarkable feature of the dynamics of the model is the existence of tristability. In fact, the system simultaneously presents three stable limit cycles. These results generalize some previous knowledge on the subject since both prey defense and a generalist predator are incorporated in our analysis.

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