CCII and FPGA Realization: A Multistable Modified Fourth-Order Autonomous Chua’s Chaotic System with Coexisting Multiple Attractors

Abstract EN

In this paper, a multistable modified fourth-order autonomous Chua’s chaotic system is investigated.

In addition to the dynamic characteristics of the third-order Chua’s chaotic system itself, what interests us is that this modified fourth-order autonomous Chua’s chaotic system has five different types of coexisting attractors: double-scroll, single band chaotic attractor, period-4 limit cycle, period-2 limit cycle, and period-1 limit cycle.

Then, an inductorless modified fourth-order autonomous Chua’s chaotic circuit is proposed.

The active elements as well as the synthetic inductor employed in this circuit are designed using second-generation current conveyors (CCIIs).

The reason for using CCIIs is that they have high conversion rate and operation speed, which enable the circuit to work at a higher frequency range.

The Multisim simulations confirm the theoretical estimates of the performance of the proposed circuit.

Finally, using RK-4 numerical algorithm of VHDL 32-bit IQ-Math floating-point number format, the inductorless modified fourth-order autonomous Chua’s chaotic system is implemented on FPGA for the development of embedded engineering applications based on chaos.

The system is simulated and synthesized on Virtex-6 FPGA chip.

The maximum operating frequency of modified Chua’s chaotic oscillator based on FPGA is 180.180 MHz.

This study demonstrates that the hardware-based multistable modified fourth-order autonomous Chua’s chaotic system is a very good source of entropy and can be applied to various embedded systems based on chaos, including secure communication, cryptography, and random number generator.