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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. [ABSTRACT FROM AUTHOR]

Because of the advent of discrete memristor, memristor effect in discrete map has become the important subject deserving discussion. To this end, this paper constructs a memristor-based neuron model considering magnetic induction by combining an existing map-based neuron model and a discrete memristor with absolute value memductance. Taking the coupling strength and initial state of the memristor as variables, complex mode transition behaviors induced by the introduced memristor are disclosed using numerical methods, including spiking-bursting behaviors, mode transition behaviors, and hyperchaotic spiking behaviors. In particular, all of these behaviors are greatly dependent on the memristor initial state, resulting in the existence of extreme multistability in the memristive neuron model. Therefore, this memristive neuron model can be used to effectively imitate the magnetic induction effects when complex mode transition behaviors appear in the neuronal action potential. Besides, a hardware platform based on FPGA is developed for implementing the memristive neuron model and various spiking-bursting sequences are experimentally captured therein. The results show that when biophysical memory effect is present, the memristive neuron model can better represent the firing activities of biological neurons than the original map-based neuron model. [ABSTRACT FROM AUTHOR]

The membrane potential difference between two adjacent neurons can induce an electromagnetic induction current that behaves like a memristor synapse effect using to couple these two neurons. Based on two-dimensional (2D) Hindmarsh-Rose (HR) neuron and non-ideal threshold memristor, this paper presents a five-dimensional (5D) neuron model of two adjacent neurons coupled by memristive electromagnetic induction. With the 5D memristor-coupled neuron model, the equilibrium states and their stabilities are investigated by qualitative analyses, and the coexisting phenomena of multiple firing patterns and initials-depending bifurcation routes along with extreme events are then uncovered by numerical simulations. Due to complex stabilities of the seven equilibrium states, the attraction basin of one neuron in the 5D memristor-coupled neuron model is not only related to the coupling strength of memristor synapse but also associated with another neuron initials, leading to that the coexisting multiple firing patterns are emerged from different regions in the attraction basin and the bifurcation routes are closely dependent to the initials. Furthermore, circuit syntheses using the off-the-shelf components and breadboard experiments for the proposed 5D memristor-coupled neuron model are executed so that the coexisting multiple firing patterns and extreme events are then conformed perfectly, which have not yet been previously reported in the coupled HR neuron model. [ABSTRACT FROM AUTHOR]