Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays by Haijun Hu, Li Liu, Jie Mao

“…The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. …”
Get full text

Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach by Yonggui Kao, Hamid Reza Karimi

“…By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. …”
Get full text

Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model by Yuhong Wang, Shulin Yang, Wuyong Qian, Xiaozhong Li

“…Taking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). …”
Get full text

A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems by A. Karimi Dizicheh, F. Ismail, M. Tavassoli Kajani, Mohammad Maleki

“…In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. …”
Get full text

Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order by Yi Chai, Liping Chen, Ranchao Wu

“…By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. …”
Get full text

Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics by Haileyesus Tessema Alemneh

“…In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. …”
Get full text

A Bright Entanglement and Squeezing Generated by an External Pumping Radiation in a Correlated Emission Laser by Chimdessa Gashu

“…The quantum and statistical properties of light generated by an external classical field in a correlated emission laser with a parametric amplifier and coupled to a squeezed vacuum reservoir are investigated using the combination of the master and stochastic differential equations. First, the solutions of the cavity-mode variables and correlation properties of noise forces associated to the normal ordering are obtained. …”
Get full text

Probability Density Evolution Algorithm for Stochastic Dynamical Systems Based on Fractional Calculus by Yang Yan, Xiaohong Yu

“…Dynamical models of the dynamic system and coupled system “three-car vehicle-rail-bridge” are established, the time-varying differential equations of motion are derived in detail, and the dynamic response of the system is calculated using the explicit Newmark algorithm. …”
Get full text

Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media by Basant K. Jha, Umaru Mohammed, Abiodun O. Ajibade

“…The resulting system of nonlinear ordinary differential equations is solved numerically using Runge Kutta-Fehlberg with shooting techniques. …”
Get full text

Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet by Meysam Mohamadali, Nariman Ashrafi

“…Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. …”
Get full text

The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes by Peng Li, Chuancun Yin, Ming Zhou

“…Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. …”
Get full text

Review on Mathematical and Mechanical Models of the Vocal Cord by L. Cveticanin

“…The corresponding mathematical models are the systems of coupled second-order differential equations which describe the vibrations of the symmetric and asymmetric vocal folds. …”
Get full text

Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control by Robert Vrabel, Pavol Tanuska, Pavel Vazan, Peter Schreiber, Vladimir Liska

“…We analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. …”
Get full text

Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension by E. Navarro, L. Jódar, R. Company

“…In this paper, we develop a Frobenius matrix method for solving higher order systems of differential equations of the Fuchs type. Generalized power series solution of the problem are constructed without increasing the problem dimension. …”
Get full text

Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy by Chao Yue, Tiecheng Xia

“…Then, the CCIRD equations are decomposed into Dubrovin-type ordinary differential equations. Furthermore, the theory of the trigonal curve and the properties of the three kinds of Abel differentials are applied to obtain the explicit theta function representations of the Baker-Akhiezer function and the meromorphic functions. …”
Get full text

The General Traveling Wave Solutions of the Fisher Equation with Degree Three by Wenjun Yuan, Qiuhui Chen, Jianming Qi, Yezhou Li

“…Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.…”
Get full text

Application of Local Fractional Homotopy Perturbation Method in Physical Problems by Nabard Habibi, Zohre Nouri

“…Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. …”
Get full text

Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument by Kuo-Shou Chiu

“…Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. …”
Get full text

On fractional Pennes bio-heat equation using Legendre collocation method by Arvind Kumar Mishra, Sushil Kumar, Ajay Kumar Shukla

“…The best feature of the proposed technique is the conversion of fractional-order differential equations into a set of algebraic systems and the ability to approximate both spatial and temporal coordinates with a single basis. …”
Get full text

An Efficient Method for Systems of Variable Coefficient Coupled Burgers’ Equation with Time-Fractional Derivative by Hossein Aminikhah, Nasrin Malekzadeh

“…Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations.…”
Get full text