When chaotic sequences are used in engineering applications, their oscillating amplitudes need to be adjusted nondestructively. To accommodate this issue, this article presents a simple 2-D sine map. It can not only generate the chaotic sequences with high complexity, but also boost the oscillating amplitudes by switching their initial states. To show the complex dynamics of the sine map, this article investigates its control parameters-related dynamical behaviors and initials-boosted coexisting bifurcations using numerical methods. The results demonstrate that the oscillating amplitudes of chaotic sequences generated by the sine map can be nondestructively controlled by switching their initial states. This makes the sine map more suitable for many chaos-based engineering applications. Furthermore, we develop a microcontroller-hardware test platform to implement the sine map. The experimental results show that the platform synchronously outputs multichannel initials-controlled chaotic sequences. We also design a pseudorandom number generator to explore the application of the sine map.

Only using one-stage op-amp based negative impedance converter realization, a simplified Chua's diode with positive outer segment slope is introduced, based on which an improved Chua's circuit realization with more simpler circuit structure is designed. The improved Chua's circuit has identical mathematical model but completely different nonlinearity to the classical Chua's circuit, from which multiple attractors including coexisting point attractors, limit cycle, double-scroll chaotic attractor, or coexisting chaotic spiral attractors are numerically simulated and experimentally captured. Furthermore, with dimensionless Chua's equations, the dynamical properties of the Chua's system are studied including equilibrium and stability, phase portrait, bifurcation diagram, Lyapunov exponent spectrum, and attraction basin. The results indicate that the system has two symmetric stable nonzero node-foci in global adjusting parameter regions and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.

High implementation complexity of multi-scroll circuit is a bottleneck problem in real chaos-based communication. Especially, in multi-scroll Chua's circuit, the simplified implementation of piecewise-linear resistors with multiple segments is difficult due to their intricate irregular breakpoints and slopes. To solve the challenge, this paper presents a systematic scheme for synthesizing a Chua's diode with multi-segment piecewise-linearity, which is achieved by cascading even-numbered passive nonlinear resistors with odd-numbered ones via a negative impedance converter. The traditional voltage mode op-amps are used to implement nonlinear resistors. As no extra DC bias voltage is employed, the scheme can be implemented by much simpler circuits. The voltage-current characteristics of the obtained Chua's diode are analyzed theoretically and verified by numerical simulations. Using the Chua's diode and a second-order active Sallen-Key high-pass filter, a new inductor-free Chua's circuit is then constructed to generate multi-scroll chaotic attractors. Different number of scrolls can be generated by changing the number of passive nonlinear resistor cells or adjusting two coupling parameters. Besides, the system can be scaled by using different power supplies, satisfying the low-voltage low-power requirement of integrated circuit design. The circuit simulations and hardware experiments both confirmed the feasibility of the designed system.