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1.
We propose a method for controlling coexisting attractors in multistable dynamical systems. In this method, the feedback for an initial duration of time can drive the system to the desired state. We have illustrated this method by considering temporal feedback in autonomous as well as non-autonomous dynamical systems. The experimental realisation of the proposed method is also presented. 相似文献
2.
The behavior of the well-known Ikeda map with very weak dissipation (so-called nearly conservative case) is investigated. The changes in the bifurcation structure of the parameter plane while decreasing the dissipation are revealed. It is shown that when the dissipation is very weak the system demonstrates an “intermediate” type of dynamics combining the peculiarities of conservative and dissipative dynamics. The correspondence between the trajectories in the phase space in the conservative case and the transformations of the set of initial conditions in the nearly conservative case has been obtained. The dramatic increase of the number of coexisting low-period attractors and the extraordinary growth of the transient time while the dissipation decreases have been revealed. The method of plotting a bifurcation tree for the set of initial conditions has been used to classify the existing attractors by their structure. Also it was shown that most of the coexisting attractors are destroyed by rather small external noise, and the transient time in noisy driven systems increases still more. The new method of two-parameter analysis for conservative systems was proposed. 相似文献
3.
In this paper, by using analysis approach and decomposition of state space, the multistability and multiperiodicity issues are discussed for Cohen-Grossberg neural networks (CGNNs) with time-varying delays and a general class of activation functions, where the general class of activation functions consist of nondecreasing functions with saturation’s including piecewise linear functions with two corner points and standard activation functions as its special case. Based on the Cauchy convergence principle, some sufficient conditions are obtained for checking the existence and uniqueness of equilibrium points of the n-neuron CGNNs. It is shown that the n-neuron CGNNs can have 2n locally exponentially stable equilibrium points located in saturation regions. Also, some conditions are derived for ascertaining equilibrium points to be locally exponentially stable or globally exponentially attractive and to be located in any designated region. As an extension of multistability, some similar results are presented for ascertaining multiple periodic orbits when external inputs of the n-neuron CGNNs are periodic. Finally, three examples are given to illustrate the effectiveness of the obtained results. 相似文献
4.
Marek Orlik 《Journal of Solid State Electrochemistry》2009,13(2):245-261
This review paper presents briefly the main concepts of nonlinear dynamics and their exemplary manifestations in selected
systems, including those important from the point of view of materials science. It is an extended version of the conference
presentation. The conditions of instabilities leading to spontaneous formation of dissipative structures are given. Principles
of nonlinear dynamics are illustrated with several examples from the homogeneous and heterogeneous and physical and chemical
systems: pattern formation in the convective motion of fluids subject to various kinds of driving forces, periodic precipitation
phenomena, oscillations, and pattern formation in the Belousov–Zhabotinski (BZ) reaction and the catalytic oxidation of thiocyanate
ions with hydrogen peroxide, as well as bistability and tristability in the electrochemical reduction of azide complexes of
nickel(II). The application of nonlinear dynamics in materials science is first exemplified by its role in polymerization
reactions. Such processes can either exhibit internal couplings leading to oscillations or can be coupled with the chemical
oscillatory process through, e.g., the covalent bonding of its catalyst to the polymer network. Other selected examples of
the application of nonlinear dynamics in materials science, referring to electrochemical processes, were briefly reviewed.
Nonlinear dynamics appears to be useful for designing new materials, including those at the nanoscale.
相似文献
Marek OrlikEmail: |
5.
We present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram (EEG). Two limit cycle attractors and one chaotic attractor were found to coexist in a two-dimensional plane of the ten-dimensional volume of initial conditions. The chaotic attractor was found to have a moderate value of the largest Lyapunov exponent (3.4 s−1 base e) with an associated Kaplan-Yorke (Lyapunov) dimension of 2.086. There are two different limit cycles appearing in conjunction with this particular chaotic attractor: one multiperiodic low amplitude limit cycle whose largest spectral peak is within the alpha band (8-13 Hz) of the EEG; and another multiperiodic large-amplitude limit cycle which may correspond to epilepsy. The cause of the coexistence of these structures is explained with a one-parameter bifurcation analysis. Each attractor has a basin of differing complexity: the large-amplitude limit cycle has a basin relatively uncomplicated in its structure while the small-amplitude limit cycle and chaotic attractor each have much more finely structured basins of attraction, but none of the basin boundaries appear to be fractal. The basins of attraction for the chaotic and small-amplitude limit cycle dynamics apparently reside within each other. We briefly discuss the implications of these findings in the context of theoretical attempts to understand the dynamics of brain function and behaviour. 相似文献
6.
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
7.
Gan Huang Jinde Cao 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2279-2289
In this paper, the multistability is studied for two-dimensional neural networks with multilevel activation functions. And it is showed that the system has n2 isolated equilibrium points which are locally exponentially stable, where the activation function has n segments. Furthermore, evoked by periodic external input, n2 periodic orbits which are locally exponentially attractive, can be found. And these results are extended to k-neuron networks, which is really enlarge the capacity of the associative memories. Examples and simulation results are used to illustrate the theory. 相似文献
8.
Prediction of the rolling behavior of ships in irregular sea remains one of the most difficult problems in ship engineering. The present work facilitates solution of this problem by derivation of a model which is meaningful from the subject-specific point of view and can efficiently be analyzed with the path-integration method. The model is a single Itô’s stochastic differential equation for the rolling angle of a ship located at a fixed spatial point. The equation appears to be of the third order and nonlinear. It takes into account the elevation of stochastic traveling sea waves. The stochasticity of the elevation is allowed for by stationary stochastic velocity of the waves. The works also notes the picture for the multistability of the derived model. Improvement of capabilities of the methods for multistable nonlinear systems is included in directions for future research. 相似文献
9.
Trajectory Segmentation and Symbolic
Representation of Dynamics of Delayed Recurrent
Inhibitory Neural Loops 下载免费PDF全文
We develop a general symbolic dynamics framework to examine the
dynamics of an analogue of the integrate-and-fire neuron model of recurrent
inhibitory loops with delayed feedback, which incorporates the firing procedure
and absolute refractoriness. We first show that the interaction of the delay, the
inhibitory feedback and the absolute refractoriness can generate three basic
types of oscillations, and these oscillations can be pinned together to form
interesting coexisting periodic patterns in the case of short feedback duration.
We then develop a natural symbolic dynamics formulation for the segmentation
of a typical trajectory in terms of the basic oscillatory patterns, and use this
to derive general principles that determine whether a periodic pattern can and
should occur. 相似文献
10.