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