Grid Multiscroll Hyperchaotic Attractors Based on Colpitts Oscillator Mode with Controllable Grid Gradient and Scroll Numbers

Abstract

Through introducing two piecewise-linear triangular wave functions in a three-dimensional spiral chaotic Colpittsoscillator model, a four-dimensional grid multiscroll hyperchaotic system is constructed. Interestingly, by adjusting abuild-in parameter in a variable of one triangle wave function, the control of the gradient of the multiscroll grid isachieved. Whereas by deploying the zero points of the two triangular wave functions to extend the saddle-focusequilibrium points with index-2 in phase space the scroll numbers do not only increase along with the number ofturning points, but they can also generate arbitrary multiples of products. The basic dynamical behaviors of theproposed four-dimensional multiscroll hyperchaotic system are analyzed. Finally, the hardware experimental circuit isdesigned and the interrelated circuit implementation is realized. The experimental results are in agreement with boththeoretical analyses and numerical simulations, which verify the feasibility of the design methods.