Othman Abdullah AlmatroudUniversity of Hail · Department of Mathematics
Othman Abdullah Almatroud
Doctor of Philosophy
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58
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Publications
Publications (58)
This work employs the Extended Direct Algebraic Method (EDAM) to solve quadratic and cubic nonlinear Klein–Gordon Equations (KGEs), which are standard models in particle and quantum physics that describe the dynamics of scaler particles with spin zero in the framework of Einstein’s theory of relativity. By applying variables-based wave transformati...
This paper introduces a modified Morris–Lecar neuron model that incorporates a memristor with a ReLU-based activation function. The impact of the memristor on the dynamics of the ML neuron model is analyzed using bifurcation diagrams and Lyapunov exponents. The findings reveal chaotic behavior within specific parameter ranges, while increased magne...
This paper presents a new third-order symmetric difference equation transformed into a 3D discrete symmetric map. The nonlinear dynamics and symmetry of the proposed map are analyzed with two initial conditions for exploring the sensitivity of the map and highlighting the influence of the map parameters on its behaviors, thus comparing the findings...
In this research paper, we delve into the analysis of a generalized discrete reaction-diffusion system. Our study begins with the discretization of a generalized reaction-diffusion model, achieved through second-order and 𝐿1-difference approximations. We explore the local stability of its unique solution, both in the absence and presence of the dif...
We explore an oscillator with nonlinear functions and equilibrium lines that displays chaos.
The equilibrium stability and complexity of the oscillator have been analysed and investigated. The
presence of multiple equilibrium lines sets it apart from previously reported oscillators. The synchronization
of the oscillator is considered as an applicat...
This paper introduces and explores the dynamics of a novel three-dimensional (3D) fractional map with hidden dynamics. The map is constructed through the integration of a discrete sinusoidal memristive into a discrete Duffing map. Moreover, a mathematical operator, namely, a fractional variable-order Caputo-like difference operator, is employed to...
This work investigates the dynamics of discrete reaction-diffusion Gierer-Meinhardt system as mathematical models of biological pattern formation. We study the system's local asymptotic behaviour with and without the diffusion once developing the discrete integer variant of the well-known Gierer-Meinhardt model and proving that the model has a uniq...
In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaot...
The use of the advancements in memristor technology to construct chaotic maps has garnered significant research attention in recent years. The combination of memristors and nonlinear terms provides an effective approach to proposing novel maps. In this study, we have leveraged memristors and sine terms to develop three-dimensional maps, capable of...
Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper...
A memristor is a two-terminal passive electronic device that exhibits memory of resistance. It is essentially a resistor with memory, hence the name “memristor”. The unique property of memristors makes them useful in a wide range of applications, such as memory storage, neuromorphic computing, reconfigurable logic circuits, and especially chaotic s...
Given the recent advances regarding the studies of discrete fractional calculus, and the fact that the dynamics of discrete-time neural networks in fractional variable-order cases have not been sufficiently documented,herein, we consider a novel class of discrete-time fractional-order neural networks using discrete nabla operator of variable-order....
Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most of the papers have been related to simulated results on the system dynamics rather
than on their hardware implementations. This work reports the implementation of a new chaotic
fractional memristor map with “hidden attractors”. The fractional...
Chaotic maps have simple structures but can display complex behavior. In this paper, we apply discrete memristance and a nonlinear term in order to design new memristive maps. A general model for constructing memristive maps has been presented, in which a memristor is connected in serial with a nonlinear term. By using this general model, different...
Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-...
Self-excited and hidden chaotic attractors are interesting complex dynamical phenomena. Here, Matouk’s hyperchaotic systems are shown to have self-excited and hidden chaotic attractors, respectively. Two case studies of hidden chaotic attractors are provided which are examined with orders 3.08 and 3.992, respectively. Moreover, self-excited chaotic...
In this article, we develop a technique to determine the analytical result of some Kaup–Kupershmidt equations with the aid of a modified technique called the new iteration transform method. This technique is a mixture of the novel integral transformation Elzaki transformation and the new iteration technique. The nonlinear term can be handled easily...
Oscillations and oscillators appear in various fields and find applications in numerous areas. We present an oscillator with infinite equilibria in this work. The oscillator includes only nonlinear elements (quadratic, absolute, and cubic ones). It is different from common oscillators, in which there are linear elements. Special features of the osc...
Dynamics and control of discrete chaotic systems of fractional-order have received considerable attention over the last few years. So far, nonlinear control laws have been mainly used for stabilizing at zero the chaotic dynamics of fractional maps. This article provides a further contribution to such research field by presenting simple linear contr...
In this paper, we consider the stochastic fractional-space Chiral nonlinear Schrödinger equation (S-FS-CNSE) derived via multiplicative noise. We obtain the exact solutions of the S-FS-CNSE by using the Riccati equation method. The obtained solutions are extremely important in the development of nuclear medicine, the entire computer industry and qu...
This paper proposes a novel continuous-time robust direct adaptive controller for the attitude control of the three-dimensional unknown chaotic spacecraft system. It considers that the plant’s nonlinear terms, exogenous disturbances, and model uncertainties are unknown and bounded; the controller design is independent of the system’s nonlinear term...
Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit is designed to mimic the oscil...
At present, the extreme multistability of fractional order neural networks are gaining much interest from researchers. In this paper, by utilizing the fractional ℑ-Caputo operator, a simple fractional order discrete-time neural network with three neurons is introduced. The dynamic of this model are experimentally investigated via the maximum Lyapun...
The aim of this paper is to deduce the asymptotic and Hille-type criteria of the dynamic equations of third order on time scales. Some of the presented results concern the sufficient condition for the oscillation of all solutions of third-order dynamical equations. Additionally, compared with the related contributions reported in the literature, th...
The storage of thermal energy in a trapezoidal aluminum enclosure via melting of PCM phase change material is studied. Experimental observations and numerical simulation are made to examine the process for the phase change of paraffin wax. The development of LHTES: latent heat thermal energy storage system is a promising alternate option to manage...
A steady non-Newtonian Carreau fluid model is considered over a two-dimensional, semi-wide, extended nonlinear stretching surface with thermal radiation effects. By applying the hypothesis of boundary layers alongside all notions, we have a structure of PDEs in our legislation such as the law of conservation of mass, momentum, energy and concentrat...
An analysis for heat transfer enhancement of Graphene oxide (Go)/Kerosene oil and Go + silver (Ag)/Kerosene oil hybrid nanofluid is made theoretically when the fluids flow through a porous medium over a stretching sheet in the presence of an applied magnetic field. The heat energy is augmented with thermal dissipation, heat source, and convective b...
The study of the chaotic dynamics in fractional-order discrete-time systems has received great attention in the past years. In this paper, we propose a new 2D fractional map with the simplest algebraic structure reported to date and with an infinite line of equilibrium. The conceived map possesses an interesting property not explored in literature...
In biological instruments, medicines and agriculture, the agglomeration of nanofluids and biotechnological mechanisms can offer significant advantages. The nanofibers, nanowires, droplets are more useful in the field of nanotechnology. There is a significant demand for nanotechnology and one can expect that the future of these materials is very bri...
This paper investigates the anti–synchronization problem between two different fractional-order chaotic and hyperchaotic systems using the modified adaptive sliding mode control technique in the presence of uncertain system parameters. To construct the proposed scheme, a simple sliding surface is first designed. Then, the modified adaptive sliding-...
This article presents some new inequalities of Simpson’s type for differentiable functions by using $(\alpha ,m) $-convexity. Some results for concavity are also obtained. These new estimates improve on the previously known ones. Some applications for special means of real numbers are also provided.
Modeling glucose-insulin regulatory system plays a key role for treating diabetes, a serious health problem for numerous patients. The effect of the incommensurate fractional-order derivatives on a glucoseinsulin regulatory model is studied in this work. It has been shown that the model exhibits some interesting dynamics, such as chaos and coexisti...
Some endeavors have been recently dedicated to explore the dynamic properties of the fractional-order discrete-time chaotic systems. To date, attention has been mainly focused on fractional-order discrete-time systems with “self-excited attractors.” This paper makes a contribution to the topic of fractional-order discrete-time systems with “hidden...
This paper proposes a new robust adaptive sliding mode control (RASMC) technique and investigates the control of chaos in the two-dimensional uncertain spin-orbit problem of Enceladus (SOPE) in the presence of external disturbances and model uncertainties. The external disturbances, model uncertainties, and nonlinear terms of the system are bounded...
This article proposes a new fractional–order discrete–time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system are
experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as 0–1 test and Approximate Entropy (ApEn) are included to de...
In this paper, the groundwork of some thermophysical properties of higher-order chemical processing and dissipation of viscous on nanofluid along with a continuously stretching porous sheet is taken. The porous medium is considered with two space coordinates, laminar, time-invariant, MHD incompressible Newtonian nanofluid. The equations are framed...
It is well-known that fractional-order discrete-time systems have a
major advantage over their integer-order counterparts, because they can bet-
ter describe the memory characteristics and the historical dependence of the
underlying physical phenomenon. This paper presents a novel fractional-order
triopoly game with bounded rationality, where th...
The bond incident degree (BID) indices can be written as a linear combination of the number of edges xi,j with end vertices of degree i and j. We introduce two transformations, namely, linearizing and unbranching, on catacondensed pentagonal systems and show that BID indices are monotone with respect to these transformations. We derive a general ex...
Nonlinear differential equations are used for describing many phenomena
in the real world as prey predator interactions. Prey predator models are classified
as one of the most important applications in applied mathematics. In this paper, modified structure of prey predator model is used, theoretical properties of the model
are presented, the bounde...
In this article, we construct an optimal family of iterative methods for finding the single root and then extend this family for determining all the distinct as well as multiple roots of single-variable nonlinear equations simultaneously. Convergence analysis is presented for both the cases to show that the optimal order of convergence is 4 in the...
A rotating MHD flow of electrically conducting Oldroyd-B fluid through non-Darcy porous medium across a stretching/shrinking surface is investigated in purview of bioconvection effects. The fluid velocity field, temperature field, concentration of nano materials and that of bio microorganisms have been simultaneously formulated in the form of coupl...
Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that th...
A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary condition...
In this paper, we considered a mathematical model concerned with the treatment of Chronic Lymphocytic Leukemia (CLL) taking into account the effect of superficially infused T cells in this particular type of tumor. The model is described thoroughly by the system of non-linear differential equations explaining the interaction of naïve, infected, can...
This article investigates a modified adaptive sliding-mode controller to achieve synchronisation between two different fractional-order chaotic systems with fully unknown parameters. A suitable parameter updating law is designed to tackle the unknown parameters. For constructing the modified adaptive sliding-mode control, a simple sliding surface i...
The purpose of this paper is to demonstrate numerically the effect of modern diet on the functions of the immune system such as modifying, identifying and inhibiting the pathogens in an unhealthy model by the intervention of vitamins within thirty days. This paper used ordinary differential equations to formulate the model which contains two popula...
This paper investigates the adaptive dual synchronization of completely different four chaotic and hyperchaotic systems with unknown parameters. Based on the Lyapunov stability theory, an efficient adaptive synchronization controller is constructed that converges the synchronization error signals to the origin with sufficient transient speed. Suita...
Function projective dual synchronization between two pairs of hyperchaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the Lyapunov stability theory, a suitable and effective adaptive control law and parameters update rule for unknown parameters are designed, such that function projective du...
In this paper, a nonlinear control scheme is developed to study the dual anti–synchronization behavior between a pair of hyperchaotic systems. This nonlinear control controller is designed based on Lyapunov stability theory and an analytic expression of the controller is shown. The nonlinear dual anti–synchronization between a pair of hyperchoatic...
This paper mainly concerns with the general methods for the function projective dual synchronization of a pair of chaotic systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of a pair of chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stabilit...
This paper addresses the dual synchronization behavior between a pair of chaotic systems via nonlinear feedback controller. On the basis of the Lyaponuv theory, a suitable and effective nonlinear feedback controller is designed, such that the dual synchronization of two pair of chaotic systems is achieved. Theoretical analysis and simulation result...
In this paper, an adaptive control scheme is developed to study the dual anti-synchronization behavior between two chaotic systems with fully uncertain parameters. This adaptive anti–synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. T...
The existence of the dual synchronization behavior between a pair of chaotic and hyperchaotic systems is investigated via a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The sufficient conditions for achieving the dual synchronization behavior between a pair of chaotic and hyperchaotic s...
The adaptive dual synchronization problem of chaotic and hyperchaotic systems with fully uncertain parameters is addressed in this paper. The sufficient conditions for achieving the dual synchronization of two chaotic and hyperchaotic systems are derived based on Lyapunov stability theory. An adaptive controller associated with the parameters updat...
The aim of this paper is to determine the structure of the dihedral groups of order 2 m+1 , where m is a natural number greater than 1, and to describe a lot of properties for these groups.