Search · four archives
Search · four archives
18 papers · ranked by Valyu relevance
Mathew O. Aibinu, Surendra Thakur, Sibusiso Moyo
a Institute for Systems Science & KZN E-Skill CoLab, Durban University of Technology, Durban 4000, South Africa bDSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa cNational Institute for Theoretical and Computational Sciences (NITheCS), South Africa dKZN E-Skill CoLab…
Andrei D. Polyanin
nonlinear PDEs and delay PDEs Authors: ['Andrei D. Polyanin'] Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related equations. It is…
Mark A. Pinsky
Instability of Some Nonlinear Systems with Delays and Variable Coefficients Authors: ['Mark A. Pinsky'] Abstract. This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed…
M. A. Elfouly, T. S. Amer
Movement disorders, like Parkinson’s disease, happen because of unusual patterns in the connections between the cortex and basal ganglia, often caused by timing issues in feedback pathways. This study uses a two-delay nonlinear dynamic model, based on the delayed the van der Pol oscillator, to examine how delays in the…
A.V. Paraskevov
Starting with the classical biophysical Morris-Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the…
Andrei D. Polyanin, Nikolay A. Kudryashov
For the first time, Schr¨odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such nonlinear equations and mathematical models are expressed. One-dimensional nonsymmetry…
Pushpendra Kumar, Dumitru Baleanu, Vedat Suat Erturk, Mustafa Inc + 1 more
'V. Govindaraj'] We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point…
Chavda Divyesh Vinodbhai, Shruti Dubey
In this paper, an efficient orthogonal neural network (ONN) approach is introduced to solve the higher-order neutral delay differential equations (NDDEs) with variable coefficients and multiple delays. The method is implemented by replacing the hidden layer of the feed-forward neural network with the orthogonal…
Dongmei Xia, Kaiyuan Chen, Lin Sun, Guojin Qin
This study delves into neutral-type systems (NTSs), emphasizing the critical role of defining precise reachable set (RS) boundaries for safe and efficient system design and operation. The investigation notably addresses the challenges posed by time-varying delays, applying Lyapunov’s direct method alongside advanced…
Mark A. Pinsky
and Stability Analysis Authors: ['Mark A. Pinsky'] Abstract. This paper introduces a new method for assessing the boundedness and stability of certain vector nonlinear systems with delays and variable coefficients. The approach is based on developing scalar counterparts to the given vector systems. We prove that the…
M. A. Elfouly, T. S. Amer
Biological motor circuits are shaped by pathway-specific delays that generate history-dependent oscillations and short-lived transients not captured by memoryless models. We develop a delayed Van der Pol in which the delay ratio r acts as a control parameter for Hopf bifurcation and internal resonance and we pair it…
Quanmin Zhu, Jianhua Zhang, Weicun Zhang, José María Amigó
This study presents a general framework for the control of unknown dynamic systems with unknown input delay. A concise output feedback control system is structured with tuning stabilization/dynamic response by an output feedback low gain, removing steady state error against step reference with a feedforward gain. A…
Mark A. Pinsky
This paper develops a new approach to the assessment of the boundedness/stability of some vector nonlinear systems with delays and variable coefficients. The approach rests on the development of scalar counterparts to the original vector systems. We show that the solutions to these scalar auxiliary nonlinear equations…
Bartosz Prokop, Lendert Gelens
Periodic changes in the concentration or activity of different molecules regulate vital cellular processes such as cell division and circadian rhythms. Developing mathematical models is essential to better understand the mechanisms underlying these oscillations. Recent data-driven methods like SINDy have fundamentally…
Gemeda Tolessa Lubo, Gemechis File Duressa
Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that…
Li Zuo, Fengtai Mei
Since the nonlinear parabolic equation has many variables, its calculation process is mostly an algebraic operation, which makes it difficult to express the discrete process concisely, which makes it difficult to effectively solve the two grid algorithm problems and the convergence problem of reaction diffusion. The…
Zhihao Chen, Xin Wang, Ning Pang, Yushan Shi + 1 more
This paper focuses on the adaptive control problem of a class of uncertain time-delay nonlinear cyber-physical systems (CPSs) with both unknown time-varying deception attacks and full-state constraints. Since the sensors are disturbed by external deception attacks making the system state variables unknown, this paper…
Authors not listed
We develop a control-oriented model for manipulating calcium carbonate (CaCO3) precipitation through pH and/or dissolved CO2(aq) adjustments in a semi-batch process. We present two open-loop control strategies: first, a closed-form optimal control solution derived via Pontryagin’s Minimum Principle; and second, an…