A different manner of study synchronization between chaotic systems is presented. This is done by using two different forced coupled nonlinear circuits. The way of coupling the systems under study is different from those used in the analysis of chaos in dynamical systems of low dimensionality. The study of synchronization and how to manipulate it, is carried out through the variation of the couplings by calculating the bifurcation diagrams. We observed that for rather larger values of the coupling between the circuits it is reached total synchronization, while for small values of the coupling it is obtained, in the best of the cases, partial synchronization.
The processing of color images is of great interest, because the human perception of color is a very complex process, still not well understood. In this article, firstly the authors present an analysis of the well-known mathematical methods used to model color as a phenomenon and to process color images. We propose an adequate metric to process color images using the Minkowski or space-time metric. We propose that the processing of HSV images can be done using the HSV cone in the quaternion split algebra or the conformal geometric algebra frameworks. We show that the processing of RGB images using the Euclidean metric in the R 3 doesn't yield good results. The colors of images change by daylight, we understand this phenomenon as the color change follows the action of the Lorentz Lie group. Consequently, we formulate a new model for representing and processing color using split quaternions and space-time conformal geometric algebra. We propose new algorithms for practical color image processing: we formulate the novel Split Quaternion Fourier Transform for color image processing and we interpolate color images using Split Motors which belong to the space-time conformal geometric algebra. The experimental part proves that real color images have to be processed in the HSV cone. We show successful applications of the Quaternion Split Fourier Transform and the interpolation processing. We compare these computations using the RGB metric in the R 3 space and using the Minkowski metric in the HSV cone. This comparison shows clearly that the color image processing using the Minkowski metric in the HSV cone performs better.
The principal objective of the paper is to show the importance of the Hamiltonian in control theory. Instead of using the Lagrangian formulation of electromechanical or robotic systems, our work is focused on robot dynamics by its Hamiltonian. Using the iterative Newton–Euler, we generate the local Hamiltonians and the derivative of the moments at each joint of the robot manipulator. Thus, we can apply decentralized controllers at each joint. We compare and discuss the efficiency of the controllers. We show that the performance of the sliding modes controller is more robust than that of the PD or Bang–Bang controllers.
In this work, a master-slave configuration to obtain synchronization between the Rayleigh and the Duffing oscillators is studied. For this configuration, we analyze the system when the dissipative coupling and one that combines the elastic and dissipative couplings are used. We analyzed the coupling parameters to find the range where synchronization between the oscillators is achieved. We found synchronization in the oscillators for large values of the coupling parameter. Our numerical findings show that for the dissipative coupling, there exists partial synchronization while for the others there is complete synchronization.
In this work a master-slave configuration to obtain synchronization between the double-well Duffing-van der Pol (master system) and the three-well Φ6 Duffing oscillators (slave system) is studied. For this configuration, we analyze the system when the dissipative and one that combines the elastic and dissipative couplings are used. Whenever the dissipative coupling is used, we observed a vertical shift synchronization in the slave system. However, when the combination of the elastic and dissipative couplings is used, the vertical shift disappears obtaining complete synchronization. We resort to perturbation method to corroborate analytically these kind of synchronization, when the master system provides an harmonic function to the slave system. These synchronizations are numerically corroborated.
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