Also, the kaplanyorke dimension\ud of the 3d novel chaotic system is obtained as dky 2. Thus, the kaplan yorke dimension \ud of the 3d novel chaotic system is easily seen as 3. 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. Lyapunov exponents toolbox let provides a graphical user interface for users to determine the full sets of lyapunov exponents and lyapunov dimension of. For a matlab package that finds lagrangian coherent structures using ftle, please refer to lcstool. In order to understand the dynamical behavior of the mnecs, the bifurcation plots are derived for three cases as follows. 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. Analysis, synchronisation and circuit implementation of a novel jerk. Hyperchaos, adaptive control and synchronization of a novel 4. A study of the nonlinear dynamics of human behavior and its. Dynamics of the new 3d chaotic system is investigated also numerically using largest lyapunov exponents spectrum and bifurcation diagrams. 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. Since the\ud sum of the lyapunov exponents is zero, the 3d novel chaotic system is conservative. The kaplanyorke dimension of the new jerk chaotic system is found as.
The qualitative properties of the novel jerk chaotic system are described in detail and matlab plots are shown. For the parameter values and initial conditions chosen in this work, the. Does anyone know of matlab scripts i could use andor adapt. My goal is to calculate the kaplan yorke dimension, and determine if the system is hyperchaotic. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. For the filtered denoised numerical and experimental.
Kaplanyorke dimension of attractor, versus download scientific. The dynamical properties of the new chaotic system are described in terms of phase portraits, lyapunov exponents, kaplanyorke dimension, dissipativity, etc. The kaplan yorke dimension of this novel hyperchaotic system is found as dky 3. 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. This section also elaborates on lyapunov exponentials, kaplan yorke dimension, equilibrium points and jacobian matrix of the proposed chaotic system. The kaplan yorke dimension of a chaotic system is defined as where is the maximum integer such that. The\ud lyapunov exponents of the 3d novel chaotic system are obtained as l1 11. A novel chaotic hidden attractor, its synchronization and. Since the sum of the lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Furthermore, control algorithms are designed for the complete synchronization of the identical hyperchaotic systems. The kaplan yorke dimension of the new jerk chaotic system is found as dky 2. The exact lyapunov dimension kaplanyorke dimension formula of the global attractor can.
The probability of a lyapunov exponent l i to be a true exponent is given by. We announce a new 4d hyperchaotic system with four parameters. A 3d novel hidden chaotic attractor with no equilibrium point is proposed in this paper. This paper reports the finding of a new threedimensional chaotic system with four quadratic nonlinear terms. Citeseerx document details isaac councill, lee giles, pradeep teregowda. These are available on all it services classroom pcs and can also be download by members of the university onto their personal pcs. Lyapunov exponents, kaplanyorke dimension, and bifurcation. The henon map, sometimes called henonpomeau attractormap, is a discretetime dynamical system. 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. Basics dynamical characteristics and properties are studied such as equilibrium points, lyapunov exponent spectrum, kaplanyorke dimension.
Jan 12, 2019 in this paper, a new 3d chaotic dissipative system is introduced. We present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram eeg. 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. 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. It has been tested under windows and unix and may also run on other platforms. I tried matlab code for bifurcation diagram to rossler. A new 3d jerk chaotic system with two cubic nonlinearities and its. Computer exercise for the chaos course the du ng oscillator. Dky represents an upper bound for the information dimension of the system. How to calculate the kaplanyorke dimension for a 4d. A software tool for the analysis and simulation of.
A new 3d jerk chaotic system with two cubic nonlinearities. Bifurcation of the time delayed system with its delay factor is investigated along with the parameter space bifurcation. How to calculate the kaplan yorke dimension for a 4d chaotic system with one positive, one zero and two negative lyapunov exponents. Matlab numerical simulations for the different three categories are. Adaptive control of the 3d novel conservative chaotic system with unknown parameters inthissection. This matlab application called caos suite allows students to simulate the. Sensitive dependence on the initial condition time t 1. The phase portraits of the novel chaotic system simulated using\ud matlab depict the chaotic attractor of the novel system. It can be shown however that the hausdorffbesicovitch dimension of this set is 5.
It is easy to deduce that for the 3d conservative chaotic system 1, the kaplan yorke dimension is given by dky 3. It is named after a kneading operation that bakers apply to dough. 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. Citeseerx note on the kaplanyorke dimension and linear. The matlab licence is for the program, plus the following standard and additional toolboxes.
The henon map takes a point x n, y n in the plane and maps it to a new point. 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. Citeseerx note on the kaplan yorke dimension and linear. A new threedimensional chaotic system is presented with its basic properties such as equilibrium points, lyapunov. In applied mathematics, the kaplanyorke conjecture concerns the dimension of an attractor, using lyapunov exponents. Matlab simulations are depicted to illustrate the phase portraits of the novel jerk. The kaplanyorke dimension of the novel jerk chaotic system is. Experimental observations and circuit realization of a jerk. The dynamic properties of the proposed hyperchaotic system are studied in detail. Lyapunov exponents of a nonlinear system define the convergence and divergence of the states. The phase portraits of the novel chaotic system simulated using matlab depict the chaotic attractor of. The exercise can be done on any computer with matlab installed. The existence of a positive lyapunov exponent confirms the chaotic behavior of the system 38, 39.
A new 3d chaotic system with four quadratic nonlinear terms. Comparison of the multisim result and matlab simulations. The kaplan yorke dimension of the novel jerk chaotic system is obtained as dky 2. The phase portraits of the jerk chaotic system simulated using matlab, depict the strange chaotic attractor\ud of the system. A new 4d hyperchaotic system with high complexity sciencedirect. Note on the kaplanyorke dimension and linear transport. Analysis and adaptive control of a novel 3d conservative no. A 3d novel highly chaotic system with four quadratic. How to calculate the kaplanyorke dimension for a 4d chaotic.
The lorenz system is a system of ordinary differential equations first studied by edward lorenz. The phase portraits of the novel chaotic system, which are obtained in this work by using matlab, depict the fourscroll attractor of the system. How to calculate the kaplanyorke dimension for a 4d chaotic system with one positive, one zero and two negative lyapunov exponents. Pdf dynamics, circuit design and fractionalorder form of a. Fractional order memristor no equilibrium chaotic system with. To enhance the applicability of the proposed system, an electronic circuit is designed by using the multisim software.
We can see that the kaplanyorke dimension is between 3. The lyapunov dimension and its estimation via the leonov method. Download scientific diagram kaplanyorke dimension of attractor, versus. Analysis, dynamics and adaptive control synchronization of a. Next, an adaptive controller is designed to stabilize the novel 4d hyperchaotic system with unknown system. In dynamical systems theory, the bakers map is a chaotic map from the unit square into itself. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Finitetime lyapunov dimension and hidden attractor of the. 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. This toolbox can only run on matlab 5 or higher versions of matlab. 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. Can a polynomial interpolation improve on the kaplanyorke. 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. What would be the bestsimplest way to calculate the full spectrum of lyapunov exponents.
Matlabsimulink model of proposed chaotic system download. It also has a graphical user interface, which is very easy to use that contains a. So the hausdorffbesicovitch dimension hasnt got this problem. This work\ud also analyses systems fundamental properties such as dissipativity, equilibria, lyapunov exponents and kaplanyorke\ud dimension. A novel chaotic system for secure communication applications.
An indirect robust adaptive nonlinear controller for complete synchronization andor control of the new system considered with mismatch disturbances is designed. 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. We would like to show you a description here but the site wont allow us. A statistical approach to estimate the lyapunov spectrum in. Chaos and generalised multistability in a mesoscopic model of. Two limit cycle attractors and one chaotic attractor were found to coexist in a twodimensional plane of the tendimensional volume of initial conditions. Indirect robust adaptive nonlinear controller design for a. Sdamala toolbox file exchange matlab central mathworks. If you find this code useful, please consider citing the accompanying paper. Kaplan and yorke proposed a dimension based on the lyapunov exponents 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. For systems in one, two or three dimensions in real variable.
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