Qualitative Study of a Novel Nonlinear Difference Equation of a General Order
Ahmed Sayed Etman,
Ahmed Essam Hammad
Issue:
Volume 11, Issue 1, February 2023
Pages:
1-6
Received:
30 November 2022
Accepted:
26 December 2022
Published:
10 January 2023
Abstract: Difference equations play a key role in analyzing many natural phenomena. Difference equations have many applications in different areas such as economic, biological physics, engineering, ecology, physiology, population dynamics and social sciences. Difference equations could also be used to simplify the dynamical systems represented by differential equations. So there exist rapid interest in investing the dynamics of the solutions of the difference equations. There exist different forms of difference equations including rational, nonlinear, max type and system of difference equations. In this paper, a novel nonlinear difference equation of general order is introduced and some qualitative properties of its solutions are studied. The parameters and the initial conditions of the difference equation are assumed to be positive real numbers. New results concerning the periodicity, semicycles, boundedness and global asymptotically stability are established. We prove that the proposed difference equation has unique positive equilibrium point. The periodic solutions with period two are studied. The semicycle analysis of the proposed difference equation is provided. The boundedness of the solutions is investigated. We give upper and lower bounds on the solutions in terms of the parameters of the proposed difference equation. Moreover, the local and global stability are investigated. Some numerical examples are provided to illustrate our results. The proposed difference equation is of general order, so the obtained results could be used for many difference equations.
Abstract: Difference equations play a key role in analyzing many natural phenomena. Difference equations have many applications in different areas such as economic, biological physics, engineering, ecology, physiology, population dynamics and social sciences. Difference equations could also be used to simplify the dynamical systems represented by differentia...
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Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay
Fangjing Zheng,
Zhifeng Lu
Issue:
Volume 11, Issue 1, February 2023
Pages:
7-16
Received:
25 December 2022
Accepted:
19 January 2023
Published:
6 February 2023
Abstract: In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable piecewise Lyapunov-Krasovskii (L-K) functional which has double integral terms, some novel sufficient criteria are put forward with the average dwell time (ADT) technique, so that the estimation error system is finite-time boundedness (FTB). It is crucial to notice that the estimation results in our work are time-delay dependent, which depend on the leakage delay as well as the upper bound of the time-varying delays. The results show that the unknown gain matrix of the state estimator is achieved by solving a series of linear matrix inequalities (LMIs), which can be effortlessly tested with the MATLAB Toolbox. Moreover, by combining with free weight matrix method in the proof process, the results we obtained do not require the differentiability of time-varying delays any more, which is less conservative than some existing results. Finally, an example is performed with its numerical simulations to corroborate the efficiency of the theoretical results.
Abstract: In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable pie...
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