共查询到19条相似文献,搜索用时 171 毫秒
1.
An experiment of dynamical behaviours in an erbium-doped fibre-ring laser with loss modulation 下载免费PDF全文
This paper reports a systematic experimental investigation on the
dynamics in the low-frequency region in an erbium-doped fibre-ring
laser with loss modulation. A rich variety of bifurcation is
analyzed through the bifurcation diagram and structured with the
concept of the winding numbers. The coexistence of multiple
attractors and the crisis that appear in the saddle-node
bifurcations, and an interesting structure of bifurcation which is
similar to the bifurcations in high-frequency range, have been
observed. 相似文献
2.
Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system 下载免费PDF全文
A new four-dimensional quadratic smooth autonomous chaotic
system is presented in this paper, which can exhibit periodic orbit
and chaos under the conditions on the system parameters.
Importantly, the system can generate one-, two-, three- and
four-scroll chaotic attractors with appropriate choices of
parameters. Interestingly, all the attractors are generated only by
changing a single parameter. The dynamic analysis approach in the
paper involves time series, phase portraits, Poincar\'{e} maps,
a bifurcation diagram, and Lyapunov exponents, to investigate some
basic dynamical behaviours of the proposed four-dimensional system. 相似文献
3.
A crisis in a Duffing--van del Pol system with fuzzy
uncertainties is studied by means of the fuzzy generalised cell
mapping (FGCM) method. A crisis happens when two fuzzy attractors
collide simultaneously with a fuzzy saddle on the basin boundary as
the intensity of fuzzy noise reaches a critical point. The two fuzzy
attractors merge discontinuously to form one large fuzzy attractor
after a crisis. A fuzzy attractor is characterized by its global
topology and membership function. A fuzzy saddle with a complicated
pattern of several disjoint segments is observed in phase space. It
leads to a discontinuous merging crisis of fuzzy attractors. We
illustrate this crisis event by considering a fixed point under
additive and multiplicative fuzzy noise. Such a crisis is fuzzy
noise-induced effects which cannot be seen in deterministic
systems. 相似文献
4.
A novel inductance-free nonlinear oscillator circuit with a single bifurcation parameter is presented in this paper. This circuit is composed of a twin-T oscillator, a passive RC network, and a flux-controlled memristor. With an increase in the control parameter, the circuit exhibits complicated chaotic behaviors from double periodicity. The dynamic properties of the circuit are demonstrated by means of equilibrium stability, Lyapunov exponent spectra, and bifurcation diagrams. In order to confirm the occurrence of chaotic behavior in the circuit, an analog realization of the piecewise-linear flux-controlled memristor is proposed, and Pspice simulation is conducted on the resulting circuit. 相似文献
5.
Determination of the exact range of the value of the parameter corresponding to chaos based on the Silnikov criterion 下载免费PDF全文
Based on the Silnikov criterion, this paper studies a
chaotic system of cubic polynomial ordinary differential equations
in three dimensions. Using the Cardano formula, it obtains the exact
range of the value of the parameter corresponding to chaos by means
of the centre manifold theory and the method of multiple scales
combined with Floque theory. By calculating the manifold near the
equilibrium point, the series expression of the homoclinic orbit is
also obtained. The space trajectory and Lyapunov exponent are
investigated via numerical simulation, which shows that there is
a route to chaos through period-doubling bifurcation and that chaotic
attractors exist in the system. The results obtained here mean
that chaos occurred in the exact range given in this paper.
Numerical simulations also verify the analytical results. 相似文献
6.
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincare′ map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. 相似文献
7.
FANGJian-Shu LIUWing-Ki ZHANLi-Xin 《理论物理通讯》2005,44(1):61-64
The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically. 相似文献
8.
A one-dimensional array of 2N + 1 automata with FitzHugh-Nagumo dynamics, in which one is set to be oscillatory and the others are excitable, is investigated with hi-directional interactions. We find that 1 : 1 rhythm propagation in the array depends on the appropriate couple strength and the excitability of the system. On the two sides of the 1 : 1 rhythm area in parameter space, two different kinds of dynamical behaviour of the pacemaker, i.e. phase-locking phenomena and canard-like phenomena, are shown. The latter is found in company with chaotic pattern and period doubling bifurcation. When the coupling strength is larger than a critical value, the whole system ends to a steady state. 相似文献
9.
Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops 下载免费PDF全文
A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincar'e map of the system is constructed. Using the Poincar'e map and the Gram-Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown. 相似文献
10.
Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap 下载免费PDF全文
Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically. 相似文献
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13.
Atiyeh Bayani Karthikeyan Rajagopal Abdul Jalil M. Khalaf Sajad Jafari G.D. Leutcho J. Kengne 《Physics letters. A》2019,383(13):1450-1456
Analyzing chaotic systems with coexisting and hidden attractors has been receiving much attention recently. In this article, we analyze a four dimensional chaotic system which has a plane as the equilibrium points. Also this system is of the group of systems that have coexisting attractors. First, the system is introduced and then stability analysis, bifurcation diagram and Largest Lyapunov exponent of this system are presented as methods to analyze the multistability of the system. These methods reveal that in some ranges of the parameter, this chaotic system has three different types of coexisting attractors, chaotic, stable node and limit cycle. Some interesting dynamics properties such as reversals of period doubling bifurcation and offset boosting are also presented. 相似文献
14.
运用广义胞映射图方法研究两个周期激励作用下Duffing-van der Pol系统的全局特性.发现了系统的混沌瞬态以及两种不同形式的瞬态边界激变, 揭示了吸引域和边界不连续变化的原因. 瞬态边界激变是由吸引域内部或边界上的混沌鞍和分形边界上周期鞍的稳定流形碰撞产生.第一种瞬态边界激变导致吸引域突然变小, 吸引域边界突然变大; 第二种瞬态边界激变使两个不同的吸引域边界合并成一体.此外, 在瞬态合并激变中两个混沌鞍发生合并, 最后系统的混沌瞬态在内部激变中消失. 这些广义激变现象对混沌瞬态的研究具有重要意义.
关键词:
广义胞映射图方法
Duffing-van der Pol
混沌瞬态
广义激变 相似文献
15.
In this paper, a novel first-order delay differential equation capable of generating n-scroll chaotic attractor is presented. Hopf bifurcation of the introduced n-scroll chaotic system is analytically and numerically determined. The bifurcation diagram and Lyapunov spectrum of the system are calculated and the results show that the system has a chaotic regime in a wider parameter range. Furthermore, period-3 behavior has been observed on the system. Circuit realizations of two-, three-, four-, and five-scroll chaotic attractors are also presented. 相似文献
16.
Novel four-dimensional autonomous chaotic system generating one-, two-, three- and four-wing attractors 下载免费PDF全文
In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the Poincaré map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations are in good agreement with the numerical simulation results. 相似文献
17.
提出了一种构造多翼蝴蝶混沌吸引子的新方法,在Liu混沌系统的基础上,通过设计一种新的分段线性函数,构造了一个产生多翼蝴蝶混沌吸引子的混沌系统,对系统的平衡点、Lyapunov指数谱、分岔图、相图、频谱和Poincare截面进行了分析。最后,设计了相应的硬件电路,电路实验结果与数值仿真结果一致,验证了该方法的可行性和有效性。 相似文献
18.
在神经起步点记录到加周期分岔过程的生理实验数据,在对此分岔过程中位于周期n爆发 和周期(n+1)爆发之间的混沌的峰峰间期数据检测不稳定的周期轨道时,发现从靠近周期 n爆发的混沌的峰峰间期数据中,可以检测出不稳定的周期n轨道;而从靠近周期(n+1)爆 发的混沌的峰峰间期数据中,不仅可以检测出不稳定的周期(n+1)轨道,还可以检测出不稳 定的周期n轨道.针对该现象,借助于Sherman建议的胰腺β细胞模型,从非线性动力 学角度给出了理论解释.指明了由鞍结分岔和倍周期分岔分别产生第一类阵发和第三类阵发 为出现该
关键词:
峰峰间期
不稳定的周期轨道
鞍结分岔
倍周期分岔 相似文献
19.
A novel 3D fractional-order chaotic system is proposed in this paper. And the system equations consist of nine terms including four nonlinearities. It's interesting to see that this new fractional-order chaotic system can generate one-wing, two-wing, three-wing and four-wing attractors by merely varying a single parameter. Moreover, various coexisting attractors with respect to same system parameters and different initial values and the phenomenon of transient chaos are observed in this new system. The complex dynamical properties of the presented fractional-order systems are investigated by means of theoretical analysis and numerical simulations including phase portraits, equilibrium stability, bifurcation diagram and Lyapunov exponents, chaos diagram, and so on. Furthermore, the corresponding implementation circuit is designed. The Multisim simulations and the hardware experimental results are well in accordance with numerical simulations of the same system on the Matlab platform, which verifies the correctness and feasibility of this new fractional-order chaotic system. 相似文献