Recurrent neural networks (RNNs) have many applications in classification, optimization, signal and image processing, pattern recognition, system identification, cryptography, and so on. These applications are highly dependent on the dynamical properties of the networks, making the analysis of the dynamical behavior an important part in the design of RNNs.
Also, neural networks (NNs) were extended to hypercomplex domains, yielding hypercomplex-valued NNs, which have caught the attention of researchers in the past years, due to their increasing number of applications.
Thus, the project aims at studying the stability and synchronization of quaternion, octonion, Clifford, and matrix-valued RNNs. Sufficient conditions given in terms of linear matrix inequalities for the stability and synchronization, using different control schemes, of quaternion-valued Hopfield and fractional-order (FO) NNs, of octonion-valued Hopfield and FO NNs, and of Clifford-valued Hopfield and FO NNs with neutral-type, leakage, time-varying, and distributed delays on time scales (TS) will be derived using techniques and methods extended from the real- and complex-valued domains. Finally, all the previously obtained results will be generalized to study the stability and synchronization of matrix-valued Hopfield and BAM NNs with delays on TS. Numerical simulations of various examples will illustrate the effectiveness of the obtained theoretical results and their easiness of use for practical applications.
The project obtained sufficient conditions for the stability and synchronization properties of Hopfield and fractional-order quaternion-, octonion-, Clifford-, and matrix-valued neural networks defined on time scales and with different types of delays. These results enable and facilitate the design of highly efficient neural networks that can be used in many areas such as associative memories, pattern and image recognition, secure communication, cryptography, etc. The publications obtained within this project give visibility to research in this scientific field carried out in Romania and increase the potential for external funding and international collaboration.
The most important results of the project are two lemmas for studying the dynamic properties of time scale systems with neutral delays and neutral and infinite distributed delays, respectively, as they can be used in subsequent papers to obtain sufficient criteria for the dynamic properties of neural networks defined on time scales. It is thus expected that the articles in which the two lemmas appeared will form the basis for further developments.