Initial-offset-boosted coexisting hyperchaos in a 2D memristive Chialvo neuron map and its application in image encryption

Designing a low-dimensional discrete map to generate chaotic sequence with the properties of high randomness and without chaos degradation is an attractive but challenging issue. The hyperchaotic dynamics of a low-dimensional discrete map can effectively solve this issue. To hit the issue, this paper introduces a memristor with sinusoidal mem-conductance function and hyper-tangent function modulated input into the one-dimensional (1D) Chialvo neuron map, thereby builds a two-dimensional (2D) memristive Chialvo neuron map with hyperchaotic dynamics. The stability and dynamical behaviors are disclosed by theoretical analysis and numerical simulation. Interestingly, the 2D memristive Chialvo neuron map can generate initial-offset boosting behavior. The forming mechanism of initial-offset boosting behavior is theoretically investigated. The results show that homogenous coexisting chaotic/hyperchaotic attractors can be regulated along memristor variable axis and boosted with the same periodicity of the sine mem-conductance. Besides, the homogenous coexisting chaotic/hyperchaotic attractors are experimentally captured on a FPGA-based digital platform. What’s more, a new encrypt algorithm is designed by employing the hyperchaotic sequences to encrypt an image. The multiple indicators and National Institute of Standards and Technology (NIST) test results show that the hyperchaotic sequences and encryption algorithm display good performance in image encryption.