This paper presents a multistable discrete memristor that is based on the discretization of a continuous-time model. It has been observed that the discrete memristor model is capable of preserving the characteristics of the continuous memristor model. Furthermore, a three-dimensional memristor discrete-time FitzHugh–Nagumo model is constructed by integrating the discrete memristor into a two-dimensional FitzHugh–Nagumo (FN) neuron model. Subsequently, the dynamic behavior of the proposed neuron model is analyzed through Lyapunov exponents, phase portraits, and bifurcation diagrams. The results show multiple kinds of coexisting hidden attractor behaviors generated by this neuron model. The proposed approach is expected to have significant implications for the design of advanced neural networks and other computational systems, with potential applications in various fields, including robotics, control, and optimization.

The $\omega$ -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified $\omega$ -distance mapping to introduce the notion of rational ${(\alpha ,\beta )}_{\phi }$ - $m\omega$ contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example.

Fixed point theory has garnered significant interest due to its applicability across various scientific disciplines. In this manuscript, we present fixed point theorems pertaining to neutrosophic fuzzy quasi-contractions, situated within the sophisticated framework of neutrosophic fuzzy metric spaces. Furthermore, we establish several fixed point results pertinent to this field of research.

We introduce a new computational model to solve efficient problems. This research generalizes the concept of bipolar fuzzy soft sets (BFSS) to the realm of complex numbers. However, the ranges of positive and negative values membership BFSS functions are extended to unit disk instead of [0, 1] and [-1, 0] respectively. The main benefit of bipolar complex fuzzy soft sets BCFSSs appears in the ability to transfer bipolar fuzzy soft information to a mathematical formula without losing the full meaning of information that may appear from different phases. Some basic operations and theorems on BCFSS are defined with numerical examples. This research has extended to illustrate the utilization of BCFSS in decision making problems by generalizing the applications and algorithms.

In this manuscript, we present the concept of E -Geraghty contractions, demonstrating several fixed point results.Additionally, we provide an illustrative example to highlight our principal findings.