A.V. Bondarev1, V.N. Efanov2, A.A. Kuchkarova3

1–3 Branch of the FSBI of Higher Education “Ufa University of Science and Technology” (Kumertau, Russia)

2 efanov@mail.ru

Formulation of the problem. A system of nonlinear equations describing the current-voltage characteristic of a memristor, the input data of which can strongly depend on various parameters, cannot be solved using the methods available in standard mathematics. Interval analysis methods developed to date are based on the use of arithmetic operations with real and complex numbers. The value of interval solutions lies in the fact that they generally allow one to obtain the most reliable solutions to the original problems, taking into account the possible ranges of changes in the initial and calculated values. Purpose of the study is tstudy the stability of nanoelectronic structures based on memristor elements under conditions of uncertain external influences. The article discusses the issues of assessing the robustness of memristor elements in order to increase the stability of their performance in nanoelectronic structures. The main idea of interval analysis is to replace arithmetic operations and real functions on real numbers with interval operations and functions that transform intervals containing these numbers. In interval analysis, the main object of study is the interval, which is a closed numerical interval. Interval analysis methods developed to date are based on the use of arithmetic operations with real and complex numbers. The use of interval analysis can help reduce errors in calculations and data storage in electronic devices. For example, when using memristors to store information, interval analysis can help take into account factors that influence errors in reading and writing data. Interval arithmetic allows you to take into account possible errors and uncertainties that may arise during measurements and calculations. This helps reduce the likelihood of errors and increase the accuracy of memristor performance predictions. The developed generalized structural-parametric model of a memristor allows us to evaluate all possible changes in the characteristics of the devices under study and avoid the need to go through all possible combinations of parameters when searching for the best option.

Bondarev A.V., Efanov V.N., Kuchkarova A.A. Development of structural-topological mathematical model of memristor for robustness analysis. Nonlinear World. 2024. V. 22. № 1. P. 56-63. DOI: https://doi.org/10.18127/j20700970-202401-07 (In Russian)

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