ترغب بنشر مسار تعليمي؟ اضغط هنا

Fractal analysis of Hopf bifurcation at infinity

110   0   0.0 ( 0 )
 نشر من قبل Goran Radunovi\\'c
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English
 تأليف Goran Radunovic




اسأل ChatGPT حول البحث

Using geometric inversion with respect to the origin we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann sphere. We study its basic properties, and apply it to the study of the Hopf-Takens bifurcation at infinity.



قيم البحث

اقرأ أيضاً

We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I) a random attractor with uniform synchronisation of trajectories, (II) a random attractor with non-uniform synchronisation of trajectories and (III) a random attractor without synchronisation of trajectories. The random attractors in phases (I) and (II) are random equilibrium points with negative Lyapunov exponents while in phase (III) there is a so-called random strange attractor with positive Lyapunov exponent. We analyse the occurrence of the different dynamical phases as a function of the linear stability of the origin (deterministic Hopf bifurcation parameter) and shear (ampitude-phase coupling parameter). We show that small shear implies synchronisation and obtain that synchronisation cannot be uniform in the absence of linear stability at the origin or in the presence of sufficiently strong shear. We provide numerical results in support of a conjecture that irrespective of the linear stability of the origin, there is a critical strength of the shear at which the system dynamics loses synchronisation and enters phase (III).
In this paper, we show the existence of Hopf bifurcation of a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the species, we sho w that when the dispersal rate tends to zero, the limit of the Hopf bifurcation value is the minimum of the local Hopf bifurcation values over all patches. On the other hand, when the dispersal rate tends to infinity, the Hopf bifurcation value tends to that of the average model.
In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1) by directly studying the Floquet multipliers and 2) by use of the Hopf bifurcation theorem. We also propose an extension of the Pyragas control scheme for which the controlled system becomes a functional differential equation of neutral type. Using the observation that we are able to determine the direction of bifurcation by a relatively simple calculation of the root tendency, we find stability conditions for the periodic orbit as a solution of the neutral type equation.
In this paper, we consider a general reaction-diffusion system with nonlocal effects and Neumann boundary conditions, where a spatial average kernel is chosen to be the nonlocal kernel. By virtue of the center manifold reduction technique and normal form theory, we present a new algorithm for computing normal forms associated with the codimension-two double Hopf bifurcation of nonlocal reaction-diffusion equations. The theoretical results are applied to a predator-prey model, and complex dynamic behaviors such as spatially nonhomogeneous periodic oscillations and spatially nonhomogeneous quasi-periodic oscillations could occur.
125 - Erxi Zhu , Min Xu , Dechang Pi 2021
Time-delay chaotic systems refer to the hyperchaotic systems with multiple positive Lyapunov exponents. It is characterized by more complex dynamics and a wider range of applications as compared to those non-time-delay chaotic systems. In a three-dim ensional general Lorenz chaotic system, time delays can be applied at different positions to build multiple heterogeneous Lorenz systems with a single time delay. Despite the same equilibrium point for multiple heterogeneous Lorenz systems with single time delay, their stability and Hopf bifurcation conditions are different due to the difference in time delay position. In this paper, the theory of nonlinear dynamics is applied to investigate the stability of the heterogeneous single-time-delay Lorenz system at the zero equilibrium point and the conditions required for the occurrence of Hopf bifurcation. First of all, the equilibrium point of each heterogeneous Lorenz system is calculated, so as to determine the condition that only zero equilibrium point exists. Then, an analysis is conducted on the distribution of the corresponding characteristic equation roots at the zero equilibrium point of the system to obtain the critical point of time delay at which the system is asymptotically stable at the zero equilibrium point and the Hopf bifurcation. Finally, mathematical software is applied to carry out simulation verification. Heterogeneous Lorenz systems with time delay have potential applications in secure communication and other fields.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا