اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe stability and Hopf bifurcation of the diffusive Nicholsons blowflies model in spatially heterogeneous environment
58
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we consider the diffusive Nicholsons blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the death rate affects the dynamics of the model. The unique positive steady state is locally asymptotically stable if the ratio is less than a critical value. However, when the ratio is greater than the critical value, large time delay can make the unique positive steady state unstable through Hopf bifurcation. Especially, the first Hopf bifurcation value tends to that of the average DDE model when the diffusion rate tends to infinity. Moreover, we show that the direction of the Hopf bifurcation is forward, and the bifurcating periodic solution from the first Hopf bifurcation value is orbitally asymptotically stable, which improves the earlier result by Wei and Li (Nonlinear. Anal., 60: 1351-1367, 2005).
قيم البحث
اقرأ أيضاً
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.
The Kuramoto model of coupled second order damped oscillators on convergent sequences of graphs is analyzed in this work. The oscillators in this model have random intrinsic frequencies and interact with each other via nonlinear coupling. The connect
ivity of the coupled system is assigned by a graph which may be random as well. In the thermodynamic limit the behavior of the system is captured by the Vlasov equation, a hyperbolic partial differential equation for the probability distribution of the oscillators in the phase space. We study stability of mixing, a steady state solution of the Vlasov equation, corresponding to the uniform distribution of phases. Specifically, we identify a critical value of the strength of coupling, at which the system undergoes a pitchfork bifurcation. It corresponds to the loss of stability of mixing and marks the onset of synchronization. As for the classical Kuramoto model, the presence of the continuous spectrum on the imaginary axis poses the main difficulty for the stability analysis. To overcome this problem, we use the methods from the generalized spectral theory developed for the original Kuramoto model. The analytical results are illustrated with numerical bifurcation diagrams computed for the Kuramoto model on ErdH{o}s--Renyi and small-world graphs. Applications of the second-order Kuramoto model include power networks, coupled pendula, and various biological networks. The analysis in this paper provides a mathematical description of the onset of synchronization in these systems.
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.
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 spher
e. We study its basic properties, and apply it to the study of the Hopf-Takens bifurcation at infinity.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
