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ABSTRACT: Through introducing two piecewise-linear triangular wave functions into a three-dimensional spiral chaotic Colpitts oscillator model, a four-dimensional grid multi-scroll hyperchaotic system is constructed. Interestingly, by adjusting a build-in parameter in a variable of one triangle wave function, the control of the gradient of the multi-scroll grid is achieved. Meanwhile, by deploying the zero points of the two triangular wave functions to extend the saddle-focus equilibrium points with index-2 in phase space, the scroll numbers not only increase along with the number of turning points, but also can generate arbitrary multiples of products. The basic dynamical behaviors of the proposed four-dimensional multi-scroll hyperchaotic system are analyzed. Finally, the hardware experimental circuit is designed and the interrelated circuit implementation is realized. The experimental results are in agreement with both theoretical analyses and numerical simulations, which verify the feasibility of the design methods.

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RESUMEN: A trav¨¦s de la introducci¨®n de dos tramos lineales funciones de onda triangular en una espiral en tres dimensiones ca¨®tico modelo de oscilador Colpitts, una de cuatro dimensiones la red multi-scroll sistema de hiperca¨®ticos se construye. Curiosamente, mediante el ajuste de una acumulaci¨®n en el par¨¢metro en una variable de una funci¨®n de onda triangular, el control de la gradiente de la cuadr¨ªcula de m¨²ltiples desplazamiento se consigue. Mientras tanto, mediante el despliegue de los puntos de cero de las dos funciones de onda triangular para extender los puntos focales de equilibrio de silla de montar con ¨ªndice-2 en el espacio de fase, no los n¨²meros de desplazamiento s¨®lo aumentan junto con el n¨²mero de puntos de inflexi¨®n, pero tambi¨¦n puede generar m¨²ltiplos arbitrarios de productos. Los comportamientos b¨¢sicos din¨¢micos de la propuesta de cuatro dimensiones multi-scroll sistema de hiperca¨®ticos se analizan. Por ¨²ltimo, el circuito experimental de hardware se ha diseñado y la implementaci¨®n de circuitos relacionados entre s¨ª se realiza. Los resultados experimentales est¨¢n de acuerdo con los dos an¨¢lisis te¨®ricos y simulaciones num¨¦ricas, que verificar la viabilidad de los m¨¦todos de diseño.
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