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101.
In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right‐hand side depending only on the past. We extend the results from paper by U. Fory? (Appl. Math. Lett. 2004; 17 (5):581–584), where the right‐hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
102.
马楠 《数学的实践与认识》2009,39(9)
研究了一类时滞离散动力系统的一次截断系统,仔细分析其分支行为和混沌性态等定性行为.与原系统进行比较,证明二者主要的定性行为非常相似.最后对未来工作提出几点建议. 相似文献
103.
The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obtained as two parameters vary. Some weak resonant and non-resonant double Hopf bifurcation phenomena are observed due to the vanishing of the real parts of two pairs of characteristic roots on the margins of the “death island” regions simultaneously. By applying the center manifold theory, the normal forms near the double Hopf bifurcation points, as well as classifications of local dynamics are analyzed. Furthermore, some quasi-periodic and chaotic motions are verified in both theoretical and numerical ways. 相似文献
104.
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction. 相似文献
105.
One of the most well-known situations in which nonlinear effects must be taken into account to obtain realistic results is
the rotating beam problem. This problem has been extensively studied in the literature and has even become a benchmark problem
for the validation of nonlinear formulations. Among other approaches, the substructuring technique was proven to be a valid
strategy to account for this problem. Later, the similarities between the absolute nodal coordinate formulation and the substructuring
technique were demonstrated. At the same time, it was found the existence of a critical angular velocity, beyond which the
system becomes unstable that was dependent on the number of substructures. Since the dependence of the critical velocity was
not so far clear, this paper tries to shed some light on it. Moreover, previous studies were focused on a constant angular
velocity analysis where the effects of Coriolis forces were neglected. In this paper, the influence of the Coriolis force
term is not neglected. The influence of the reference conditions of the element frame are also investigated in this paper. 相似文献
106.
Haixia Wang Qishao Lu Qingyun Wang 《Communications in Nonlinear Science & Numerical Simulation》2008,13(8):1668-1675
Bursting is an important electrical behavior in neuron’s firing. In this paper, based on the fast/slow dynamical bifurcation analysis and the phase plane analysis, two types of bursting are presented in the modified Morris–Lecar neuronal model, and the associated bifurcation mechanisms of switching between the active phase and the silent phase are analyzed. For two coupled bursters, it is found that the same type of coupled bursters may have different synchronization transition path from that of two different types of coupled bursters. The analysis of bursting types and the transition to synchronization may provide us with better insight into neuronal encoding and information transmission. 相似文献
107.
Passively Q-switched microchip lasers generate strongly pulsating intensity oscillations that emerge from a Hopf bifurcation point. We show that this bifurcation is nearly vertical and explain why strongly pulsating oscillations are immediately observed as we pass the Hopf bifurcation point. The laser dynamical problem is mathematically a singular perturbation problem which we investigate. The leading order problem is conservative and corresponds to Lotka–Volterra equations. 相似文献
108.
To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic. 相似文献
109.
110.