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Codimension-one and -two bifurcation analysis of a discrete-time prey-predator model
This paper investigates bifurcations analysis and resonances in a discrete-time prey-predator model analytically and numerically as well. The local...
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Codimension-one and codimension-two bifurcations in a new discrete chaotic map based on gene regulatory network model
In this paper, the stability and bifurcations of a new discrete chaotic map based on gene regulatory network are studied. Firstly, the existence and...
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Investigating the dynamics of bursting by combining two fast–slow analyses with codimension-2 bifurcations in the embryonic pre-BötC neuron model
The network activity of the pre-Bötzinger complex (pre-BötC) in the mammalian brainstem controls the inspiratory phase of the respiratory rhythm....
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A double-zero bifurcation in a Lorenz-like system
The Lorenz system presents a double-zero bifurcation (a double-zero eigenvalue with geometric multiplicity two). However, its study by means of...
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Bifurcation Analysis of Systems With Delays: Methods and Their Use in Applications
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation...
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Bogdanov–Takens bifurcation of an enzyme-catalyzed reaction model
Enzyme-catalyzed reactions are frequently observed in the chemical process, and could be described by the mathematical model, such as the Gray–Scott...
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Bifurcation and path-following continuation analysis of periodic orbits of an extended Fermi oscillator model
In this research, we offer eigenvalue analysis and path following continuation to describe the impact, stick, and non-stick between the particle and...
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Bursting types and bifurcation analysis of the temperature-sensitive Purkinje neuron
The bursting discharge behaviour of neurons is affected by many factors, among which temperature is one of the more important factors. In this work,...
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Static Bifurcation in Mechanical Control Systems
Feedback regulation of nonlinear dynamical systems inevitably leads to issues concerning static bifurcation. Static bifurcation in feedback systems...
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Bifurcation Control in Feedback Systems
In this chapter the mathematical tools from bifurcation theory are used within the framework of feedback control systems. The first part deals with a...
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Bifurcation Dynamics in Control Systems
This chapter deals with bifurcation dynamics in control systems, which are described by ordinary differential equations, partial differential...
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Singular Bautin bifurcation analysis of a slow–fast predator–prey system
Over the past few decades, the study of complex oscillations in slow–fast systems has been a focal point of research. Within the realm of slow–fast...
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Bifurcation Theory
Bifurcation theory is the study of the changes in the number of solutions and the type of solutions to models as parameters are varied. The term...
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Codimension-two border collision bifurcation in a two-class growth model with optimal saving and switch in behavior
We consider a two-class growth model with optimal saving and switch in behavior. The dynamics of this model is described by a two-dimensional (2D)...
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Distance to Bifurcation in Multidimensional Parameter Space: Margin Sensitivity and Closest Bifurcations
The problem of operating or designing a system with robust stability with respect to many parameters can be viewed as a geometric problem in...
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Slow–Fast Dynamics in a Non-smooth Vector Field with Zero-Hopf Bifurcation
PurposeThe purpose of this paper is to study the influence of non-smoothness on the slow-fast dynamics of a vector field with codimension-2 zero-Hopf...
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Bursting Oscillations Induced by Coexisted Cycles Separated by Fold Limit Cycle Bifurcation
PurposeThis study identifies the basic characteristics as well as the bifurcation mechanism of slow-fast behaviors in a typical model with two...
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Phenomenological Aspects of Bifurcation of Structures
The state-space of a mechanical system, made of positions and velocities, is introduced. In this space, the definition of stability of equilibrium is...
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Ergodic and resonant torus doubling bifurcation in a three-dimensional quadratic map
We consider the rich dynamics and bifurcations exhibited by a three-dimensional quadratic map. Torus doubling bifurcations are central to bifurcation...
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Self-sustained dynamics by modeling competing PHA-producers and non-PHA-producers bacteria population for a limited resource: local and homoclinic bifurcation analysis
We propose a mathematical model for two species competing for a limited resource associated to polyhydroxyalkanoate (PHA) production, which possesses...
