For systems with a dimension n 2 the evidence that the kaplan yorke dimension is equivalent to or provides a strong approximation of the information dimension is numerical only and less. Kaplan and yorke proposed a dimension based on the lyapunov exponents of the system. Basics dynamical characteristics and properties are studied such as equilibrium points, lyapunov exponent spectrum, kaplanyorke dimension. Computer exercise for the chaos course the du ng oscillator. Dynamics of the new 3d chaotic system is investigated also numerically using largest lyapunov exponents spectrum and bifurcation diagrams.
Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Can a polynomial interpolation improve on the kaplanyorke. A study of the nonlinear dynamics of human behavior and its. Pdf a new 4d chaotic system with hidden attractor and its. A number of new relations between the kaplan yorke dimension, phase space contraction, transport coefficients and the maximal lyapunov exponents are given for dissipative thermostatted systems, subject to a small but nonzero external field in a nonequilibrium stationary state. Bifurcation of the time delayed system with its delay factor is investigated along with the parameter space bifurcation. The phase portraits of the novel chaotic system, which are obtained in this work by using matlab, depict the fourscroll attractor of the system. When a new chaotic oscillator is introduced, it must accomplish characteristics like guaranteeing the existence of a positive lyapunov exponent and a high kaplan yorke dimension. A software tool for the analysis and simulation of. In applied mathematics, the kaplanyorke conjecture concerns the dimension of an attractor, using lyapunov exponents. The paper starts with a detailed dynamic analysis of the properties of the system such as phase plots, lyapunov exponents, kaplan yorke dimension and equilibrium points. The henon map, sometimes called henonpomeau attractormap, is a discretetime dynamical system.
Numerical integration of a blob of neighboring points, calculation of finitetime lyapunov exponents and the spatial field of kaplan yorke dimensions, and animation and plotting tools. The exercise can be done on any computer with matlab installed. Furthermore, control algorithms are designed for the complete synchronization of the identical hyperchaotic systems. We can see that the kaplanyorke dimension is between 3. How to calculate the kaplan yorke dimension for a 4d chaotic system with one positive, one zero and two negative lyapunov exponents. Analysis and adaptive control of a novel 3d conservative no. So the hausdorffbesicovitch dimension hasnt got this problem. In cases where the lyapunov exponent estimation could not be achieved, the correlation dimension was approximated using the kaplanyorke dimension and was marked by a double asterisk. Bifurcation and chaos in time delayed fractional order.
Since the\ud sum of the lyapunov exponents is negative, the 3d novel chaotic system is dissipative. Sdamala toolbox file exchange matlab central mathworks. Dky represents an upper bound for the information dimension of the system. A new 4d hyperchaotic system with high complexity sciencedirect. This paper reports the finding of a new threedimensional chaotic system with four quadratic nonlinear terms.
Comparison of the multisim result and matlab simulations. A novel methodology for synchronizing identical time delayed systems with an uncertainty in the slave system is proposed and tested with the proposed time delayed fractional order chaotic memfractor oscillator. Lyapunov exponents of a nonlinear system define the convergence and divergence of the states. This research work proposes a seventerm novel 3d chaotic system with three quadratic nonlinearities and analyses the\ud fundamental properties of the system such as dissipativity, symmetry, equilibria, lyapunov exponents and kaplan yorke \ud dimension. A novel chaotic system for secure communication applications ali durdu, ahmet turan ozcerit department of computer engineering, faculty of computer and information science, sakarya university, 54187 serdivan, sakarya, turkey, email. A statistical approach to estimate the lyapunov spectrum in. Since the\ud sum of the lyapunov exponents is zero, the 3d novel chaotic system is conservative. We present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram eeg. It also has a graphical user interface, which is very easy to use that contains a. It is easy to deduce that for the 3d conservative chaotic system 1, the kaplan yorke dimension is given by dky 3. Citeseerx document details isaac councill, lee giles, pradeep teregowda. A novel chaotic hidden attractor, its synchronization and. Matlabsimulink model of proposed chaotic system download.
It is named after a kneading operation that bakers apply to dough. Indirect robust adaptive nonlinear controller design for a. Lyapunov exponents les are necessary and more convenient for detecting hyperchaos in fractional. A 3d novel hidden chaotic attractor with no equilibrium point is proposed in this paper. The kaplan yorke dimension of the new jerk chaotic system is found as dky 2.
Analysis, dynamics and adaptive control synchronization of a. In some cases, the coefficients of a mathematical model can be varied to increase the values of those characteristics but it is not a trivial task because a very huge number of combinations arise and the required. This toolbox can only run on matlab 5 or higher versions of matlab. Lyapunov exponents toolbox let provides a graphical user interface for users to determine the full sets of lyapunov exponents and lyapunov dimension of continuous and discrete chaotic systems. It can be shown however that the hausdorffbesicovitch dimension of this set is 5. We announce a new 4d hyperchaotic system with four parameters. Two limit cycle attractors and one chaotic attractor were found to coexist in a twodimensional plane of the tendimensional volume of initial conditions. The kaplanyorke dimension of the novel jerk chaotic system is.
The kaplanyorke dimension of the new jerk chaotic system is found as. Finitetime lyapunov dimension and hidden attractor of the. Chaos and generalised multistability in a mesoscopic model of. My goal is to calculate the kaplan yorke dimension, and determine if the system is hyperchaotic. Since the sum of the lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. The dynamical properties of the new chaotic system are described in terms of phase portraits, lyapunov exponents, kaplanyorke dimension, dissipativity, etc. An indirect robust adaptive nonlinear controller for complete synchronization andor control of the new system considered with mismatch disturbances is designed. The phase portraits of the novel chaotic system simulated using matlab depict the chaotic attractor of. Fractional order memristor no equilibrium chaotic system with.
The dynamic properties of the proposed hyperchaotic system are studied in detail. For a matlab package that finds lagrangian coherent structures using ftle, please refer to lcstool. Hyperchaos, adaptive control and synchronization of a novel 4. How to calculate the kaplanyorke dimension for a 4d chaotic. The matlab licence is for the program, plus the following standard and additional toolboxes. The existence of a positive lyapunov exponent confirms the chaotic behavior of the system 38, 39. Feb 07, 2020 2 if nusigmad, where nu is the correlation exponent, sigma the information dimension, and d the hausdorff dimension, then d kaplan yorke dimension of the 3d novel chaotic system is easily seen as 3. The probability of a lyapunov exponent l i to be a true exponent is given by. We would like to show you a description here but the site wont allow us. How to calculate the kaplanyorke dimension for a 4d chaotic system with one positive, one zero and two negative lyapunov exponents. This section also elaborates on lyapunov exponentials, kaplan yorke dimension, equilibrium points and jacobian matrix of the proposed chaotic system. To enhance the applicability of the proposed system, an electronic circuit is designed by using the multisim software.
Lyapunov exponents, kaplanyorke dimension, and bifurcation. A new 3d jerk chaotic system with two cubic nonlinearities. A number of new relations between the kaplan yorke dimension, phase space contraction, transport coecients and the maximal lyapunov exponents are given for dissipative thermostatted systems, subject to a small but nonzero external eld in a nonequilibrium stationary state. The phase portraits of the jerk chaotic system simulated using matlab, depict the strange chaotic attractor\ud of the system. In order to understand the dynamical behavior of the mnecs, the bifurcation plots are derived for three cases as follows.
How to calculate the kaplanyorke dimension for a 4d. Also, the kaplanyorke dimension\ud of the 3d novel chaotic system is obtained as dky 2. Does anyone know of matlab scripts i could use andor adapt. Sensitive dependence on the initial condition time t 1. The henon map takes a point x n, y n in the plane and maps it to a new point. This work\ud also analyses systems fundamental properties such as dissipativity, equilibria, lyapunov exponents and kaplanyorke\ud dimension. Matlab numerical simulations for the different three categories are. The phase portraits of the novel chaotic system simulated using\ud matlab depict the chaotic attractor of the novel system. The dynamic behaviors of the proposed system are investigated by theoretical analysis focusing on its elementary characteristics such as lyapunov exponents, kaplan yorke dimension, attractor forms, and equilibrium points. For the parameter values and initial conditions chosen in this work, the. The qualitative properties of the novel jerk chaotic system are described in detail and matlab plots are shown. In dynamical systems theory, the bakers map is a chaotic map from the unit square into itself.
A new threedimensional chaotic system is presented with its basic properties such as equilibrium points, lyapunov. Kaplanyorke dimension of attractor, versus download scientific. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The kaplan yorke dimension of the novel jerk chaotic system is obtained as dky 2.
Citeseerx note on the kaplanyorke dimension and linear. A new 3d jerk chaotic system with two cubic nonlinearities and its. Analysis, synchronisation and circuit implementation of a novel jerk. Thus, the kaplan yorke dimension \ud of the 3d novel chaotic system is easily seen as 3. A new 3d chaotic system with four quadratic nonlinear terms. What would be the bestsimplest way to calculate the full spectrum of lyapunov exponents. The kaplan yorke dimension of this novel hyperchaotic system is found as dky 3. These are available on all it services classroom pcs and can also be download by members of the university onto their personal pcs. For systems in one, two or three dimensions in real variable. Pdf dynamics, circuit design and fractionalorder form of a. For the filtered denoised numerical and experimental. The exact lyapunov dimension kaplanyorke dimension formula of the global attractor can. A 3d novel highly chaotic system with four quadratic.
Citeseerx note on the kaplan yorke dimension and linear. The kaplan yorke dimension of a chaotic system is defined as where is the maximum integer such that. Jan 12, 2019 in this paper, a new 3d chaotic dissipative system is introduced. Download scientific diagram kaplanyorke dimension of attractor, versus. This matlab application called caos suite allows students to simulate the. If you find this code useful, please consider citing the accompanying paper. Adaptive control of the 3d novel conservative chaotic system with unknown parameters inthissection. The lorenz system is a system of ordinary differential equations first studied by edward lorenz. The lyapunov dimension and its estimation via the leonov method. I tried matlab code for bifurcation diagram to rossler. It has been tested under windows and unix and may also run on other platforms.
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