Results 51 to 60 of about 710,736 (219)

Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation

Fractal and Fractional, 2022
The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order ...
Xianghong Li, Yanli Wang, Yongjun Shen
doaj   +1 more source

Path-Connectedness in Global Bifurcation Theory [PDF]

arXiv, 2021
A celebrated result in bifurcation theory is that global connected sets of non-trivial solutions bifurcate from trivial solutions at non-zero eigenvalues of odd algebraic multiplicity of the linearized problem when the operators involved are compact. In this paper a simple example is constructed which satisfies the regularity hypotheses of the global ...
arxiv  

The Path Formulation of Bifurcation Theory [PDF]

, 1994
We show how the path formulation of bifurcation theory can be made to work, and that it is (essentially) equivalent to the usual parametrized contact equivalence of Golubitsky and Schaeffer.
openaire   +4 more sources

The Pitchfork Bifurcation [PDF]

, 2016
We give development of a new theory of the Pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.
arxiv   +1 more source

Ghost orbit bifurcations in semiclassical spectra [PDF]

Prog. Theor. Phys. Suppl. (Kyoto) 139 (2000), 429-436, 2000
Gutzwiller's semiclassical trace formula for the density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurcation (``ghost orbits'') can produce clear signatures ...
arxiv   +1 more source

The Modelling and Control of a Singular Biological Economic System in a Polluted Environment

Discrete Dynamics in Nature and Society, 2016
A singular biological economic model with harvesting and stage structure is presented. The local stability of equilibriums of the system is investigated when the economic profit parameter is zero, and the conditions of the singularity induced bifurcation
Yi Zhang, Yueming Jie, Xinyou Meng
doaj   +1 more source

Dynamics of a Discrete-Time Chaotic Lü System

Pan-American Journal of Mathematics, 2022
A discrete-time chaotic Lü system is investigated. Firstly, we give the conditions of local stability of this system around feasible fixed points. Then, we show analytically that discretized Lü system undergoes a flip-Neimark Sacker (NS) bifurcation when
Sarker Md. Sohel Rana, Md. Jasim Uddin
doaj   +1 more source

Dynamics of neural fields with exponential temporal kernel [PDF]

Theory in Biosciences, 2024, 2019
We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork ...
arxiv   +1 more source

The Bifurcation of Two Invariant Closed Curves in a Discrete Model

Discrete Dynamics in Nature and Society, 2018
A discrete population model integrated using the forward Euler method is investigated. The qualitative bifurcation analysis indicates that the model exhibits rich dynamical behaviors including the existence of the equilibrium state, the flip bifurcation,
Yingying Zhang, Yicang Zhou
doaj   +1 more source

Singular bifurcations and regularization theory

Physical Review E
Several nonlinear and nonequilibrium driven as well as active systems (e.g. microswimmers) show bifurcations from one state to another (for example a transition from a non motile to motile state for microswimmers) when some control parameter reaches a critical value.
Alexander Farutin, Chaouqi Misbah
openaire   +3 more sources