scholarly journals Assessing the Impacts of Competition and Dispersal on a Multiple Interactions Type Model

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Murtala Bello Aliyu ◽  
Mohd Hafiz Mohd ◽  
Mohd Salmi Md. Noorani
Keyword(s):  
Bifurcation Analysis ◽  
Species Coexistence ◽  
Real Life ◽  
Period Doubling ◽  
Type Model ◽  
Coexistence Mechanisms ◽  
Multiple Species ◽  
The Stability ◽  
Transcritical Bifurcations ◽  
Multiple Interactions

Multiple interactions (e.g., mutualist-resource-competitor-exploiter interactions) type models are known to exhibit oscillatory behaviour as a result of their complexity. This large-amplitude oscillation often de-stabilises multispecies communities and increases the chances of species extinction. What mechanisms help species in a complex ecological system to persist? Some studies show that dispersal can stabilise an ecological community and permit multi-species coexistence. However, previous empirical and theoretical studies often focused on one- or two-species systems, and in real life, we have more than two-species coexisting together in nature. Here, we employ a (four-species) multiple interactions type model to investigate how competition interacts with other biotic factors and dispersal to shape multi-species communities. Our results reveal that dispersal has (de-)stabilising effects on the formation of multi-species communities, and this phenomenon shapes coexistence mechanisms of interacting species. These contrasting effects of dispersal can best be illustrated through its combined influences with the competition. To do this, we employ numerical simulation and bifurcation analysis techniques to track the stable and unstable attractors of the system. Results show the presence of Hopf bifurcations, transcritical bifurcations, period-doubling bifurcations and limit point bifurcations of cycles as we vary the competitive strength in the system. Furthermore, our bifurcation analysis findings show that stable coexistence of multiple species is possible for some threshold values of ecologically-relevant parameters in this complex system. Overall, we discover that the stability and coexistence mechanisms of multiple species depend greatly on the interplay between competition, other biotic components and dispersal in multi-species ecological systems.

scholarly journals Combined Impacts of Predation, Mutualism and Dispersal on the Dynamics of a Four-Species Ecological System

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Murtala Bello Aliyu ◽  
Mohd Hafiz Mohd
Keyword(s):  
Hopf Bifurcation ◽  
Species Interactions ◽  
Species Coexistence ◽  
Biotic Interactions ◽  
Ecological System ◽  
Stable Limit ◽  
Combined Effects ◽  
Coexistence Mechanisms ◽  
Multiple Species ◽  
The Stability

Multi-species and ecosystem models have provided ecologist with an excellent opportunity to study the effects of multiple biotic interactions in an ecological system. Predation and mutualism are among the most prevalent biotic interactions in the multi-species system. Several ecological studies exist, but they are based on one-or two-species interactions, and in real life, multiple interactions are natural characteristics of a multi-species community. Here, we use a system of partial differential equations to study the combined effects of predation, mutualism and dispersal on the multi-species coexistence and community stability in the ecological system. Our results show that predation provided a defensive mechanism against the negative consequences of the multiple species interactions by reducing the net effect of competition. Predation is critical in the stability and coexistence of the multi-species community. The combined effects of predation and dispersal enhance the multiple species coexistence and persistence. Dispersal exerts a positive effect on the system by supporting multiple species coexistence and stability of community structures. Dispersal process also reduces the adverse effects associated with multiple species interactions. Additionally, mutualism induces oscillatory behaviour on the system through Hopf bifurcation. The roles of mutualism also support multiple species coexistence mechanisms (for some threshold values) by increasing the stable coexistence and the stable limit cycle regions. We discover that the stability and coexistence mechanisms are controlled by the transcritical and Hopf bifurcation that occurs in this system. Most importantly, our results show the important influences of predation, mutualism and dispersal in the stability and coexistence of the multi-species communities

APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350055 ◽  
Author(s):  
SHYAN-SHIOU CHEN ◽  
CHANG-YUAN CHENG ◽  
YI-RU LIN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Type Model ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Trapping Region ◽  
Saddle Node ◽  
The Stability ◽  
Two Equilibria

In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh–Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: (1) the number and stability of the equilibria are analyzed in detail using a table to demonstrate the matter in which the stability of the equilibrium changes and to determine which two equilibria collapse through the saddle-node bifurcation; (2) the sufficient conditions for an Andronov–Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and (3) we elaborately evaluate the sufficient conditions for the Bogdanov–Takens (BT) and Bautin bifurcations. Several numerical simulations for these conditions are also presented. In particular, two types of bistable behaviors are numerically demonstrated: the BT and Bautin bifurcations. Notably, all of the bifurcation curves in the domain of the remaining parameters are similar when the time scale is large. Additionally, to show the potential for a limit cycle, the existence of a trapping region is demonstrated. These results present a variety of diverse behaviors for this model. The results of this study will be helpful in assessing suitable parameters for fitting the resemblances of experimental observations.

scholarly journals Bifurcation Analysis of Piecewise Smooth Bimodal Maps Using Normal Form

2020 ◽  
Vol 24 (3) ◽  
pp. 137-151
Author(s):  
Z. T. Zhusubaliyev ◽  
D. S. Kuzmina ◽  
O. O. Yanochkina
Keyword(s):  
Fixed Point ◽  
Normal Form ◽  
Bifurcation Analysis ◽  
Stability Region ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Piecewise Smooth ◽  
Continuous Map ◽  
The Stability ◽  
Smooth Map

Purpose of reseach. Studyof bifurcations in piecewise-smooth bimodal maps using a piecewise-linear continuous map as a normal form. Methods. We propose a technique for determining the parameters of a normal form based on the linearization of a piecewise-smooth map in a neighborhood of a critical fixed point. Results. The stability region of a fixed point is constructed numerically and analytically on the parameter plane. It is shown that this region is limited by two bifurcation curves: the lines of the classical period-doubling bifurcation and the “border collision” bifurcation. It is proposed a method for determining the parameters of a normal form as a function of the parameters of a piecewise smooth map. The analysis of "border-collision" bifurcations using piecewise-linear normal form is carried out. Conclusion. A bifurcation analysis of a piecewise-smooth irreversible bimodal map of the class Z1–Z3–Z1 modeling the dynamics of a pulse–modulated control system is carried out. It is proposed a technique for calculating the parameters of a piecewise linear continuous map used as a normal form. The main bifurcation transitions are calculated when leaving the stability region, both using the initial map and a piecewise linear normal form. The topological equivalence of these maps is numerically proved, indicating the reliability of the results of calculating the parameters of the normal form.

Species coexistence and niche theory

2019 ◽  
pp. 141-157
Author(s):  
Gary G. Mittelbach ◽  
Brian J. McGill
Keyword(s):  
Interspecific Competition ◽  
Species Coexistence ◽  
Apparent Competition ◽  
Competing Species ◽  
Invasion Fitness ◽  
Niche Differences ◽  
Trade Offs ◽  
Coexistence Mechanisms ◽  
The Face ◽  
Multiple Species

Ecologists have long puzzled over the question of how multiple species may coexist in a community in the face of strong interspecific competition. This chapter explores the answers that modern coexistence theory provides to this question. Spatial and temporal heterogeneity in the environment, in conjunction with species differences in resource use and dispersal (niche differences and trade-offs) provide important general coexistence mechanisms. More specifically, theory shows that stable species coexistence is enhanced when intraspecific competition is stronger than interspecific competition (α‎jj>α‎ji). Recent theoretical developments show how this criteria for coexistence (α‎jj>α‎ji) is related to two different aspects of the niche. Less niche overlap between competing species provides a positive stabilizing effect on species coexistence, whereas greater equality in the invasion fitness of competing species provides a positive equalizing effect on coexistence. Analysis of models of apparent competition due to shared predation yield similar conclusions.

scholarly journals Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Lei Shi
Keyword(s):  
Asymptotic Behavior ◽  
Bifurcation Analysis ◽  
Trivial Solution ◽  
Type Model ◽  
Bifurcation Parameter ◽  
Local Behavior ◽  
Nontrivial Solutions ◽  
Ginzburg Landau ◽  
The Stability ◽  
Bifurcation And Stability

We study the bifurcation and stability of trivial stationary solution(0,0)of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain(0,L)with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the lengthLof the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.

scholarly journals Identifying route to stall flutter through stochastic bifurcation analysis

2018 ◽  
Vol 211 ◽  
pp. 02011
Author(s):  
Rajagopal V Bethi ◽  
Sai Vishal Reddy Gali ◽  
J Venkatramani
Keyword(s):  
Fluid Flow ◽  
Limit Cycle ◽  
Bifurcation Analysis ◽  
Period Doubling ◽  
Stochastic Bifurcation ◽  
Nonlinear Phenomenon ◽  
Limit Cycle Oscillations ◽  
Viscous Effects ◽  
Stall Flutter ◽  
The Stability

The interaction of an elastic structure such as an airfoil and fluid flow can give rise to nonlinear phenomenon such as limit cycle oscillations, period doubling or chaos. These phenomena are indicated by a change in the stability behaviour of the dynamical known as bifurcations. Presence of viscous effects in the fluid flow can give rise to flow separation which causes a stability change in the system that is identified to happen via a Hopf bifurcation. In such cases, the airfoil exhibits limit cycle oscillations which are torsionally dominant, known as stall flutter. Despite identifying the route to stall flutter under uniform flow conditions, investigating a stall problem under stochastic wind has received minimal attention. The ability of fluctuating flows to change the stability boundaries and disrupt the route to flutter, compels the need to carry out a stochastic analysis of stalling airfoils. Study of stall flutter in such systems under the influence of a time varying sinusoidal gust is undertaken and the route to flutter is identified by carrying out a stochastic bifurcation analysis.

Turning Dynamics: Part 1 — Experimental Analysis

2012 ◽  
Author(s):  
Eric B. Halfmann ◽  
C. Steve Suh ◽  
N. P. Hung
Keyword(s):  
Instantaneous Frequency ◽  
Period Doubling ◽  
Displacement Sensor ◽  
Laser Displacement Sensor ◽  
Turning Process ◽  
Time Frequency ◽  
Spectral Components ◽  
Tool Vibrations ◽  
Exact Moment ◽  
The Stability

The workpiece and tool vibrations in a lathe are experimentally studied to establish improved understanding of cutting dynamics that would support efforts in exceeding the current limits of the turning process. A Keyence laser displacement sensor is employed to monitor the workpiece and tool vibrations during chatter-free and chatter cutting. A procedure is developed that utilizes instantaneous frequency (IF) to identify the modes related to measurement noise and those innate of the cutting process. Instantaneous frequency is shown to thoroughly characterize the underlying turning dynamics and identify the exact moment in time when chatter fully developed. That IF provides the needed resolution for identifying the onset of chatter suggests that the stability of the process should be monitored in the time-frequency domain to effectively detect and characterize machining instability. It is determined that for the cutting tests performed chatters of the workpiece and tool are associated with the changing of the spectral components and more specifically period-doubling bifurcation. The analysis presented provides a view of the underlying dynamics of the lathe process which has not been experimentally observed before.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals Pre-Drawn Syringes of Comirnaty for an Efficient COVID-19 Mass Vaccination: Demonstration of Stability

Pharmaceutics ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1029
Author(s):  
Francesca Selmin ◽  
Umberto M. Musazzi ◽  
Silvia Franzè ◽  
Edoardo Scarpa ◽  
Loris Rizzello ◽  
...  
Keyword(s):  
Mechanical Stress ◽  
Real Life ◽  
Storage Conditions ◽  
Lipid Nanoparticles ◽  
Mass Vaccination ◽  
Hydrodynamic Diameter ◽  
The Us ◽  
Real Mass ◽  
The Stability ◽  
And Storage

Moving towards a real mass vaccination in the context of COVID-19, healthcare professionals are required to face some criticisms due to limited data on the stability of a mRNA-based vaccine (Pfizer-BioNTech COVID-19 Vaccine in the US or Comirnaty in EU) as a dose in a 1 mL-syringe. The stability of the lipid nanoparticles and the encapsulated mRNA was evaluated in a “real-life” scenario. Specifically, we investigated the effects of different storing materials (e.g., syringes vs. glass vials), as well as of temperature and mechanical stress on nucleic acid integrity, number, and particle size distribution of lipid nanoparticles. After 5 h in the syringe, lipid nanoparticles maintained the regular round shape, and the hydrodynamic diameter ranged between 80 and 100 nm with a relatively narrow polydispersity (<0.2). Samples were stable independently of syringe materials and storage conditions. Only strong mechanical stress (e.g., shaking) caused massive aggregation of lipid nanoparticles and mRNA degradation. These proof-of-concept experiments support the hypothesis that vaccine doses can be safely prepared in a dedicated area using an aseptic technique and transferred without affecting their stability.

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

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