A competition model with herd behaviour and allee effect

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2529-2542
Author(s):  
Prosenjit Sen ◽  
Alakes Maiti ◽  
G.P. Samanta
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Local Stability ◽  
Allee Effect ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Competition Model ◽  
Discrete Time Delay ◽  
Herd Behaviour

In this work we have studied the deterministic behaviours of a competition model with herd behaviour and Allee effect. The uniform boundedness of the system has been studied. Criteria for local stability at equilibrium points are derived. The effect of discrete time-delay on the model is investigated. We have carried out numerical simulations to validate the analytical findings. The biological implications of our analytical and numerical findings are discussed.

Stabilization of Linear Discrete Time Delay Systems with Additive Disturbance and Saturating Actuators

2000 ◽  
Vol 33 (14) ◽  
pp. 261-266
Author(s):  
Sophie Tarbouriech ◽  
Germain Garcia ◽  
Pedro L.D. Peres ◽  
Isabelle Queinnec
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Saturating Actuators ◽  
Discrete Time Delay

More Dynamical Properties Revealed from a 3D Lorenz-like System

2014 ◽  
Vol 24 (10) ◽  
pp. 1450133 ◽  
Author(s):  
Haijun Wang ◽  
Xianyi Li
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Mathematical Work ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Properties ◽  
Theoretical Results

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both "locally" and "globally" and both "finitely" and "infinitely" — to comprehensively explore a given system.

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