This Letter presents a new second‐order discrete map model, which is derived from a simple sampling switch‐based memristor‐capacitor circuit. The memristor‐based map model has infinite unstable and critical stable fixed points, and exhibits chaotic and hyperchaotic behaviours via a period‐doubling bifurcation scenario. These complex dynamical behaviours are confirmed by the phase portraits, iterative sequences and basins of attraction.

The continuous memristor models have been applied to various chaotic circuits. However, the discrete memristor models and their applications to discrete maps haven't attracted much attention, yet. In this brief, we first present a discrete memristor model and analyze its characteristics. By coupling the model into the Logistic map, a memristive Logistic map is further achieved. Due to the existence of line fixed point, the memristive Logistic map can be unstable or critically stable, depending on its control parameters and initial state. Using several analysis methods, we study the control parameters-relied dynamical behaviors of the memristive Logistic map and disclose its hyperchaotic attractors. The numerical results show that the discrete memristor can efficiently improve the chaos complexity in the Logistic map. In addition, digital experiments are designed to validate the numerical results.

In a cascaded power converter, the input current ripple of load converter is fed forward to the output capacitor of source converter and results in reshaping the output capacitor current and output voltage ripples of source converter. To investigate the stability effect of feedforward current ripple of load converter on source converter, a cascaded power converter comprising two peak-voltage-ripple controlled buck converters is taken as an example. First, the stability effects of chosen circuit parameters of the source converter in cascaded operation and standalone operation are demonstrated and compared. Second, by describing three switching state sequences induced by the feedforward current ripple, a discrete-time map model is established for the cascaded power converter. Based on the map model, the instability mechanism of source converter with the variations of the circuit parameters is thereby expounded, and the stability boundaries are obtained in the circuit parameter planes. The results show that the stability effects of the circuit parameters of source converter with feedforward current ripple are essentially different from those in the standalone operation. The theoretical analyses are verified by the simulation results and experimental results.

Recently, the application of memristors to improve chaos complexity in discrete chaotic systems has been paid more and more attention to. To enrich the application examples of discrete memristor-based chaotic systems, this article proposes a new three-dimensional (3-D) memristor-based Lozi map by introducing a discrete memristor into the original two-dimensional (2-D) Lozi map. The proposed map has no fixed points but can generate hidden hyperchaos, so it is a hidden hyperchaotic map. The dynamical effects of the discrete memristor on the memristor-based Lozi map and two types of coexisting hidden attractors boosted by the initial conditions are demonstrated using some numerical methods. The numerical results clearly show that the introduced discrete memristor allows the proposed map to have complicated hidden dynamics evolutions and also exhibit heterogeneous and homogeneous hidden multistability. Finally, a digital platform is used to realize the memristor-based Lozi map, and its experimental phase portraits are obtained to confirm the numerical ones.

Both constant on-time (COT) and fixed off-time (FOT) control techniques are suitable for various applications requiring fast transient response. However, the discrete-time model of COT controlled buck converter only has two switched borderlines, whereas that of FOT controlled buck converter has four switched borderlines. Based on the derivations of these borderlines, an asynchronous-switching map of FOT controlled buck converter is established. With the decrease of equivalent series resistance (ESR) of output capacitor, instability and mode shifting from continuous conduction mode (CCM) to discontinuous conduction mode (DCM) are discussed. Furthermore, with small ESR of output capacitor, stability effects of load resistance and inductance on dynamical behaviors are investigated, and the approximate stability criteria and the corresponding normalized critical conditions are obtained. The theoretical analyses and experimental results show that the converter operates in DCM chaos via period-doubling and border-collision bifurcation routes, and its instability caused by small ESR can be removed by choosing appropriate load resistance, inductance, and voltage transfer ratio, which are very suitable for the circuit design of FOT controlled buck converter.

Nonlinear activation function is the most essential factor that enables Hopfield neural networks (HNNs) to generate complex dynamics. However, less attention has been paid to the activation function. In this article, we propose a simple discrete model of self-connectionless HNN in which two heterogeneous neurons have different activation functions of sine and hyperbolic tangent. By theoretical and numerical methods, we explore coexisting bifurcation behaviors induced by Neimark-Sacker bifurcations and multifolded hyperchaotic attractors caused by multiple fixed points with different stability. We also evaluate the randomness of these multifolded hyperchaotic sequences and implement the discrete model on field programmable gate array (FPGA) hardware device. In brief, this discrete model with simple algebraic equations has the simplest connection structure under the two-heterogeneous-neuron HNN framework, but it can generate various multifolded hyperchaotic attractors with high randomness. Additionally, based on FPGA hardware device, a chaos-based hardware Poisson encoder is developed to implement the reconstruction of gray image.