## 1 Introduction  
The memristor, a condensed term for \"memory resistor\", constitutes one of the four essential components in electronic circuits, alongside resistors, capacitors, and inductors. Originating from the theoretical and mathematical work of [PERSON] in 1971 [1], the memristor operates as a nonlinear resistor with a unique memory feature. [PERSON]'s concept established a fundamental connection between electrical charge and magnetic flux linkage, providing the groundwork for understanding how the memristor's resistance, known as memristance, dynamically changes in response to the historical flow of electric charge. This dynamic behavior contrasts with the fixed resistance of conventional resistors. The theoretical foundation of the memristor concept was further associated with resistive switching devices, illustrating its natural occurrence in nanoscale systems. The physical realization of the memristor was documented in 2008 when [PERSON] and colleagues at HP LABS observed the memristor effect in a nanogrid memory array structure. This structure utilized an extremely thin layer of titanium dioxide TiO\({}_{2}\) demonstrating variable resistance modulated by the electric charge passing through it--a defining characteristic of memristors. The intrinsic properties of TiO\({}_{2}\) contributed to its suitability for memristor development [2, 3]. Following the 2008 milestone, numerous research papers (as depictedin Figure 1a) have been published, reporting the discovery of memristor-like effects in diverse structures. These findings, such as those presented by [PERSON] in 2012, continue to contribute to the evolving understanding and applications of memristive phenomena in various technological domains [4]. In the realm of memristor research, the understanding of the resistive switching mechanism has profoundly influenced the design of current devices. The durability of memristive devices has been linked to the stability of their material phases, with TaO\({}_{x}\) and HfO\({}_{x}\) identified as crucial memristive oxides for technological applications [5; 6]. The efficacy of the switching process is contingent upon factors such as the nature and distribution of defects, as well as kinetic aspects like ion mobility and redox reaction rates. For instance, in electrochemical metallization (ECM) cells, a filament-type memristor, the switching mechanism is driven by metal cations such as Ag and Cu. Conversely, in valence-change memory (VCM) cells, the movement of oxygen anions serves as the trigger for switching events. Consequently, both ECM and VCM devices exhibit bipolar switching behavior, transitioning between \"on\" and \"off\" states under opposite electrical polarities [7]. The ensuing surge in experimental studies has delved into the exploration of resistive switching effects, significantly amplifying interest in memristor technology. [PERSON] et al. reported on a resistive random-access memory (ReRAM) device, a type of memristive device, utilizing multilayer oxide heterostructures. Their findings demonstrated the systematic control of switching characteristics to enhance memory and logic applications. Through adjustments in the composition, thickness, and stacking sequence of the multilayer oxide heterostructures, diverse switching behaviors were achieved, including high cycling endurance and nonlinear on-state characteristics [8]. These advancements have paved the way for the development of memristive devices tailored to nonvolatile memory, distinguished by attributes such as high speed, scalability, low power consumption, and nonvolatile storage capabilities [9; 10; 11]. Consequently, the distinctive features of memristors have captured the scientific community's attention, prompting their exploration as promising candidates for sophisticated memory blocks [12], analog and digital processing circuits [13], and neuromorphic systems [14; 15]. Figure 1: Web of Science data showing the number of publications per year based on searched words: (**a**) Memristor. (**b**) Thermal memristor.