共查询到20条相似文献,搜索用时 15 毫秒
1.
The effects on time-simulation by automatic control of step-size is presented to simulate the behavior of Chua’s circuit, which consist of five circuit elements: one linear resistor, one inductor, two capacitors and one nonlinear resistor known as Chua’s diode. The last element is modeled by an I–V piecewise-linear function to formulate a system of state-variables equations, which are solved by applying multistep methods with automatic control of step-size to simulate the generation of chaotic phenomena. It is highlighted the speed-up in time simulation to estimate the values of the circuit elements, so that the synthesis of Chua’s diode can be realized directly using novel electronic circuits. 相似文献
2.
Jose Alvarez-Ramirez Eduardo Rodriguez Juan Carlos Echeverria Hector Puebla 《Chaos, solitons, and fractals》2008,36(5):1157-1169
Chaotic systems exhibit an erratic behavior reflected by a strong divergence of trajectories with arbitrarily close initial condition. In this way, similar to trajectories from pseudorandom number generators, chaotic trajectories can be seen as noise with some degree of correlation. This work focuses on the study of some correlation properties (i.e., scaling) of chaotic trajectories from the Chua’s system. This is done by using detrended fluctuation analysis, which is a method designed for the detection of correlations in stochastic time series. It is found that, in general, Chua’s trajectories behave as a Brownian motion for small time scales, while they can display a white noise-like behavior or be dominated by harmonic oscillations for large time scales. 相似文献
3.
An algorithm for suppressing the chaotic oscillations in non-linear dynamical systems with singular Jacobian matrices is developed using a linear feedback control law based upon the Lyapunov–Krasovskii (LK) method. It appears that the LK method can serve effectively as a generalised method for the suppression of chaotic oscillations for a wide range of systems. Based on this method, the resulting conditions for undisturbed motions to be locally or globally stable are sufficient and conservative. The generalized Lorenz system and disturbed gyrostat equations are exemplified for the validation of the proposed feedback control rule. 相似文献
4.
In this paper, we obtain a general Ekeland’s variational principle for set-valued mappings in complete metric space, which is different from those in [G.Y. Chen, X.X. Huang, Ekeland’s ε-variational principle for set-valued mapping, Mathematical Methods of Operations Research 48 (1998) 181–186; G.Y. Chen, X.X. Huang, S.H. Hou, General Ekeland’s Variational Principle for Set-Valued Mappings, Journal of Optimization Theory and Applications 106 (2000) 151–164; S.J. Li, W.Y. Zhang, On Ekeland’s variational Principle for set-valued mappings, Acta Mathematicae Application Sinica, English Series 23 (2007) 141–148]. By the result, we prove some existence results for a general vector equilibrium problem under nonconvex and compact or noncompact assumptions of its domain, respectively. Moreover, we give some equivalent results to the variational principle. 相似文献
5.
《Chaos, solitons, and fractals》2006,27(2):501-510
This paper is concerned with robust control for a class of Lorenz systems subject to mismatch uncertainties. It is implemented by using variable structure control. The proposed variable structure controller ensures the occurrence of the sliding mode for the error dynamics. It is guaranteed that under the proposed control law, uncertain Lorenz systems can drive the system state exactly to some specific points or in a predictable neighborhood of arbitrary desired points in the state space even with mismatch uncertainties, which is not addressed in the literature. 相似文献
6.
Heng Liu Lidong Wang Zhenyan Chu 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6144-6147
Let X be a complete metric space without isolated points, and let f:X→X be a continuous map. In this paper we prove that if f is transitive and has a periodic point of period p, then f is distributionally chaotic in a sequence. Particularly, chaos in the sense of Devaney is stronger than distributional chaos in a sequence. 相似文献
7.
Necessary conditions in the form of Pontryagin’s maximum principle are derived for impulsive control problems with mixed constraints. A new mathematical concept of impulsive control is introduced as a requirement for the consistency of the impulsive framework. Additionally, this control concept enables the incorporation of the engineering needs to consider conventional control action while the impulse develops. The regularity assumptions under which the maximum principle is proved are weaker than those in the known literature. Ekeland’s variational principle and Lebesgue’s discontinuous time variable change are used in the proof. The article also contains an example showing how such impulsive controls could be relevant in actual applications. 相似文献
8.
We investigate the qualitative behavior of a host‐parasitoid model with a strong Allee effect on the host. More precisely, we discuss the boundedness, existence and uniqueness of positive equilibrium, local asymptotic stability of positive equilibrium and existence of Neimark–Sacker bifurcation for the given system by using bifurcation theory. In order to control Neimark–Sacker bifurcation, we apply pole‐placement technique that is a modification of OGY method. Moreover, the hybrid control methodology is implemented in order to control Neimark–Sacker bifurcation. Numerical simulations are provided to illustrate theoretical discussion. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
9.
Qamar Din 《Journal of Difference Equations and Applications》2017,23(4):741-762
We investigate the complex behaviour of a modified Nicholson–Bailey model. The modification is proposed by Hassel and Varley taking into account that interaction between parasitoids is taken in such a way that the searching area per parasitoid is inversely proportional to the m-th power of the population density of parasitoids. Under certain parametric conditions the unique positive equilibrium point of system is locally asymptotically stable. Moreover, it is proved that system undergoes Neimark-Sacker bifurcation for small range of parameters by using standard mathematical techniques of bifurcation theory. In order to control Neimark-Sacker bifurcation, we apply simple feedback control strategy and pole-placement technique which is a modification of OGY method. Moreover, the hybrid control methodology is also implemented for chaos controlling. Numerical simulations are provided to illustrate theoretical discussion. 相似文献
10.
Let (X, d) be a compact metric space and fn : X → X a sequence of continuous maps such that (fn) converges uniformly to a map f. The purpose of this paper is to study the Devaney’s chaos on the uniform limit f. On the one hand, we show that f is not necessarily transitive even if all fn mixing, and the sensitive dependence on initial conditions may not been inherited to f even if the iterates of the sequence have some uniform convergence, which correct two wrong claims in [1]. On the other hand, we give some equivalence conditions for the uniform limit f to be transitive and to have sensitive dependence on initial conditions. Moreover, we present an example to show that a non-transitive sequence may converge uniformly to a transitive map. 相似文献
11.
The aim of this paper is the synthesis of a robust control law for chaos suppression of a class of non-linear oscillator with affine control input. A robust state observer based active controller, which provides robustness against model uncertainties and noisy output measurements is proposed. The closed-loop stability for the underlying closed-loop system is done via the regulation and estimation errors dynamics. The performance of the proposed control law is illustrated with numerical simulations. The method is general and can be applied to various non-linear systems which satisfy the conditions required. 相似文献
12.
In this paper, we revisit the chaotic number of iterations needed by Newton’s method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions, i.e. regions where the method converges nicely to a root, can be complicatedly a function of the parameter. 相似文献
13.
A.M.A. El-Sayed A. Elsaid H.M. Nour A. Elsonbaty 《Communications in Nonlinear Science & Numerical Simulation》2013,18(1):148-170
This paper is devoted to study the dynamical behavior of a modified Autonomous Van der Pol-Duffing (ADVP) circuit when its nonlinear element is replaced by a flux controlled memristor. The bifurcation diagrams, Lyapunov exponents, and phase portraits of the state variables are presented. Then, the chaos which appears at certain values of the system’s parameters is controlled using linear feedback control. Finally, the synchronization between two chaotic modified ADVP circuits is achieved in the case of fully unknown parameters of the system using adaptive synchronization. 相似文献
14.
For the multivariable control system described by \(\dot x = Ax + Bu,y = Cx,z = Dx\) (wherey is the measured output andz the output to be regulated) conditions are given for the existence of a controller which preserves output regulation and loop stability, in the presence of small parameter variations in controller and plant. Under mild conditions, such a “strong” synthesis is shown to exist if and only if the regulator problem with internal stability (RPIS) is well-posed. Synthesis is achieved by means of a feedback configuration which in general incorporates an invariant, and suitably redundant, copy of the dynamic model adopted for the exogenous disturbance and reference signals which the system is required to process. 相似文献
15.
16.
Fu-Hsiang Wong Shiueh-Ling Yu Cheh-Chih Yeh Wei-Cheng Lian 《Applied Mathematics Letters》2006,19(12):1293-1299
The purpose of this work is to establish the timescale version of Lyapunov’s inequality as follows: Let be a nontrivial solution of satisfying . Then, under suitable conditions on , , and , we have where and satisfies if . Here is a timescale (see below). 相似文献
17.
We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form we obtain the conditions of abrupt transition from an attracting fixed point to an attracting cycle or a chaotic attractor (cyclic chaotic intervals). These conditions allow us to describe the bifurcation structure of the parameter space of the map in a neighborhood of the boundary related to the border collision bifurcation of the fixed point. Particular attention is devoted to codimension-two bifurcation points. Moreover, the described bifurcation structure confirms that the chaotic attractors of the considered map are robust, that is, persistent under parameter perturbations. 相似文献
18.
O. V. Baburova V. Ch. Zhukovsky B. N. Frolov 《Theoretical and Mathematical Physics》2008,157(1):1420-1432
Based on the requirement that the gauge invariance principle for the Poincaré-Weyl group be satisfied for the space-time manifold,
we construct a model of space-time with the geometric structure of a Weyl-Cartan space. We show that three types of fields
must then be introduced as the gauge (“compensating”) fields: Lorentz, translational, and dilatational. Tetrad coefficients
then become functions of these gauge fields. We propose a geometric interpretation of the Dirac scalar field. We obtain general
equations for the gauge fields, whose sources can be the energy-momentum tensor, the total momentum, and the total dilatation
current of an external field. We consider the example of a direct coupling of the gauge field to the orbital momentum of the
spinor field. We propose a gravitational field Lagrangian with gauge-invariant transformations of the Poincaré-Weyl group.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 64–78, October, 2008. 相似文献
19.
In this paper, we study dynamics of a class of chromosome’s attractors. We show that these chromosome sequences are chaotic by giving a rigorous verification for existence of horseshoes in these systems. We prove that the Poincaré maps derived from these chromosome’s attractors are semi-conjugate to the 2-shift map, and its entropy is no less than log 2. The chaotic behavior is robust in the following sense: chaos exists when one parameter varies from −5.5148 to −5.4988. 相似文献
20.
It is well known that the Wang transform [Wang, S.S., 2002. A universal framework for pricing financial and insurance risks. Astin Bull. 32, 213–234] for the pricing of financial and insurance risks is derived from Bühlmann’s economic premium principle [Bühlmann, H., 1980. An economic premium principle. Astin Bull. 11, 52–60]. The transform is extended to the multivariate setting by [Kijima M., 2006. A multivariate extension of equilibrium pricing transforms: The multivariate Esscher and Wang transforms for pricing financial and insurance risks, Astin Bull. 36, 269–283]. This paper further extends the results to derive a class of probability transforms that are consistent with Bühlmann’s pricing formula. The class of transforms is extended to the multivariate setting by using a Gaussian copula, while the multiperiod extension is also possible within the equilibrium pricing framework. 相似文献