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The offset as the average value of a variable plays an important role in signal processing and system design. Offset boosting can be realized by a non-bifurcation parameter or an initial condition. In this work, symmetric coexisting attractors with opposite polarity and a 2D hyperchaotic map with multiple modes of offset boosting are proposed, where the offset can be controlled both by the initial condition and system parameter, and as a result, multiple alternatives of offset boosting and offset competition show up. Consequently, the final offset is determined eventually by the balance of two factors. The theoretical findings are verified through the hardware experiment based on the STM32. Finally, a pseudo-random number generator (PRNG) is constructed based on the newly proposed hyperchaotic map, demonstrating its high performance in engineering applications.

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By the combined feedback of exponential, cubic and sinusoidal nonlinearity, a hyperchaotic map is constructed, which has the distinct features as providing two unipolar hyperchaotic sequences and large area of hyperchaotic orbit. A fast video encryption algorithm that adopted the permutation-diffusion-permutation strategy was developed consequently based on the hyperchaotic system. Each frame image obtained from the video stream is encrypted by the algorithm in real time. To accelerate the encryption, the frame image are encrypted in parallel. Experiment results and security analysis confirm the good security, robustness, and effectiveness of the encryption algorithm.