共查询到20条相似文献,搜索用时 10 毫秒
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This paper formulates a new three-dimensional chaotic system that originates from the Lorenz system, which is different from the known Lorenz system, Rössler system, Chen system, and includes Lü systems as its special case. By using the center manifold theorem, the stability character of its non-hyperbolic equilibria is obtained. The Hopf bifurcation and the degenerate pitchfork bifurcation, the local character of stable manifold and unstable manifold, are also in detail shown when the parameters of this system vary in the space of parameters. Corresponding bifurcation cases are illustrated by numerical simulations, too. The existence or non-existence of homoclinic and heteroclinic orbits of this system is also studied by both rigorous theoretical analysis and numerical simulation. 相似文献
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Ma Chenguang Mou Jun Xiong Li Banerjee Santo Liu Tianming Han Xintong 《Nonlinear dynamics》2021,103(3):2867-2880
Nonlinear Dynamics - In this paper, a new four-dimensional dissipative chaotic system which can produce multiple asymmetric attractors is designed and its dynamical behaviors are analyzed. The... 相似文献
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In this paper, we introduce a new chaotic complex nonlinear system and study its dynamical properties including invariance,
dissipativity, equilibria and their stability, Lyapunov exponents, chaotic behavior, chaotic attractors, as well as necessary
conditions for this system to generate chaos. Our system displays 2 and 4-scroll chaotic attractors for certain values of
its parameters. Chaos synchronization of these attractors is studied via active control and explicit expressions are derived
for the control functions which are used to achieve chaos synchronization. These expressions are tested numerically and excellent
agreement is found. A Lyapunov function is derived to prove that the error system is asymptotically stable. 相似文献
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Karthikeyan Rajagopal Anitha Karthikeyan Ashokkumar Srinivasan 《Nonlinear dynamics》2018,91(3):1491-1512
Memristor-based chaotic and hyperchaotic systems are of great interest in the recent years, and addition of meminductor and memcapacitors to the family has widened the applications. In this paper, we propose a new chaotic system with fractional-order memristor and memcapacitor components. Nonlinear chaotic properties of the proposed system are investigated with equilibrium points, eigenvalues, Lyapunov exponents, bifurcation and bicoherence plots. We show that a small model disturbance can make the system to show self-excited and hidden attractors. We use the Adomian Decomposition method for implementing the proposed system in Field Programmable Gate Arrays. 相似文献
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Hongwei Li 《Nonlinear dynamics》2012,70(2):1327-1334
Inspirited by Li and Jin (Nonlinear Dyn. 67:2857?C2864 2012), this paper investigates the Hopf bifurcation of a four-dimensional hyperchaotic system with only one equilibrium. A detailed set of conditions are derived, which guarantee the existence of the Hopf bifurcation. Furthermore, the standard normal form theory is applied to determine the direction and type of the Hopf bifurcation, and the approximate expressions of bifurcating periodic solutions and their periods. In addition, numerical simulations are used to justify theoretical results. 相似文献
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In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China's futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic. 相似文献
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The present paper reports the design and analysis of a new time-delayed chaotic system and its electronic circuit implementation. The system is described by a first-order nonlinear retarded type delay differential equation with a closed form mathematical function describing the nonlinearity. We carry out stability and bifurcation analysis to show that with the suitable delay and system parameters the system shows sustained oscillation through supercritical Hopf bifurcation. It is shown through numerical simulations that the system depicts bifurcation and chaos for a certain range of the system parameters. The complexity and predictability of the system are characterized by Lyapunov exponents and Kaplan?CYork dimension. It is shown that, for some suitably chosen system parameters, the system shows hyperchaos even for a small or moderate delay. Finally, we set up an experiment to implement the proposed system in electronic circuit using off-the-shelf circuit elements, and it is shown that the behavior of the time delay chaotic electronic circuit agrees well with our analytical and numerical results. 相似文献
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In this paper, from the view of stability and chaos control, we investigate the Rossler chaotic system with delayed feedback.
At first, we consider the stability of one of the fixed points, verifying that Hopf bifurcation occurs as delay crosses some
critical values. Then, for determining the stability and direction of Hopf bifurcation we derive explicit formulae by using
the normal-form theory and center manifold theorem. By designing appropriate feedback strength and delay, one of the unstable
equilibria of the Rossler chaotic system can be controlled to be stable, or stable bifurcating periodic solutions occur at
the neighborhood of the equilibrium. Finally, some numerical simulations are carried out to support the analytic results. 相似文献
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S-box structures used in the encryption architecture are of great importance for constructing powerful block encryption systems, which hold an important place in modern cryptology. The design of S-boxes with sound cryptographic characteristics is of utmost importance for constructing powerful encryption systems. In this study, an S-box design algorithm based on time-delay chaotic systems is proposed. The proposed algorithm is considered relative to other algorithms in the literature as more useful according to such criteria as simplicity and efficient implementation. Theoretical analysis and computer simulations demonstrated that the proposed algorithm meets all the performance requirements for the S-box design criteria, and also verified the efficient and practical structure of the algorithm. 相似文献
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This paper introduces a novel three-dimensional autonomous chaotic system by adding a quadratic cross-product term to the first equation and modifying the state variable in the third equation of a chaotic system proposed by Cai et al. (Acta Phys. Sin. 56:6230, 2007). By means of theoretical analysis and computer simulations, some basic dynamical properties, such as Lyapunov exponent spectrum, bifurcations, equilibria, and chaotic dynamical behaviors of the new chaotic system are investigated. Furthermore, hybrid function projective synchronization (HFPS) of the new chaotic system is studied by employing three different synchronization methods, i.e., adaptive control, system coupling and active control. The proposed approaches are applied to achieve HFPS between two identical new chaotic systems with fully uncertain parameters, HFPS in coupled new chaotic systems, and HFPS between the integer-order new chaotic system and the fractional-order Lü chaotic system, respectively. Corresponding numerical simulations are provided to validate and illustrate the analytical results. 相似文献
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Ri Kwangchol Jong Yongson Yun Cholil Kim Kwangchol Han Poknam 《Nonlinear dynamics》2022,109(3):1441-1461
Nonlinear Dynamics - In this paper, the nonlinear vibration phenomena occurring in a flexible rotor supported on squeeze-film dampers (SFDs) are investigated. The complex nonlinearities caused by... 相似文献
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This paper analyzes musical opus from the point of view of two mathematical tools, namely the entropy and the multidimensional scaling (MDS). The Fourier analysis reveals a fractional dynamics, but the time rhythm variations are diluted along the spectrum. The combination of time-window entropy and MDS copes with the time characteristics and is well suited to treat a large volume of data. The experiments focus on a large number of compositions classified along three sets of musical styles, namely ??Classical??, ??Jazz??, and ??Pop & Rock?? compositions. Without lack of generality, the present study describes the application of the tools and the sets of musical compositions in a methodology leading to clear conclusions, but extensions to other possibilities are straightforward. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments toward a dynamical analysis of musical compositions. 相似文献
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Ana Dalia Pano-Azucena Jose de Jesus Rangel-Magdaleno Esteban Tlelo-Cuautle Antonio de Jesus Quintas-Valles 《Nonlinear dynamics》2017,87(4):2203-2217
The experimental realization of a chaotic secure communication system is introduced herein taking advantage of Arduino’s open source integrated development environment along with its preset functions that reduce development time and complexity. The system uses multi-directional multi-scroll chaotic oscillators that are based on piecewise-linear functions. Experimental results are given for chaos generators in 1-direction (1-D), 2-D and 3-D of up to 20, \(20\times 20\) and \(20\times 20\times 20\) scrolls, respectively. Using two chaos generators, a chaotic secure communication system is implemented in a master–slave topology by applying generalized Hamiltonian forms and observer approach. Finally, we detail experimental results for the synchronization of \(6\times 6\) and \(20\times 20\) scroll attractors, which are used for transmitting a monochromatic image through the Arduino-based chaotic secure communication system. 相似文献
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A generalized Sprott C system with only two stable equilibria is investigated by detailed theoretical analysis as well as dynamic simulation, including some basic dynamical properties, Lyapunov exponent spectra, fractal dimension, bifurcations, and routes to chaos. In the parameter space where the equilibria of the system are both asymptotically stable, chaotic attractors coexist with period attractors and stable equilibria. Moreover, the existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters is investigated. Periodic solutions and chaotic attractors can be found when these cycles disappear. 相似文献
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This paper presents a new periodic switching chaotic system, which is topologically non-equivalent to the original sole chaotic systems. Of particular interest is that the periodic switching chaotic system can generate stable solution in a very wide parameter domain and has rich dynamic phenomena. The existence of a stable limit cycle with a suitable choice of the parameters is investigated. The complex dynamical evolutions of the switching system composed of the Rössler system and the Chua’s circuit are discussed, which is switched by equal period. Then the possible bifurcation behaviors of the system at the switching boundary are obtained. The mechanism of the different behaviors of the system is investigated. It is pointed out that the trajectories of the system have obvious switching points, which are decided by the periodic signal. Meanwhile, the system may be led to chaos via a period-doubling bifurcation, resulting in the switching collisions between the trajectories and the non-smooth boundary points. The complicated dynamics are studied by virtue of theoretical analysis and numerical simulation. Furthermore, the control methods of this periodic switching system are discussed. The results we have obtained clearly show that the nonlinear switching system includes different waveforms and frequencies and it deserves more detailed research. 相似文献