Article
Engineering, Mechanical
Chunyan Gao, Fangqi Chen
Summary: The study demonstrates that transcription and translation delays act as bifurcation parameters driving oscillation behavior in a gene expression model, with their length determining the amplitude and period of the oscillations. Optimal parameter rates are also crucial for inducing limit-cycle oscillations. Additionally, transcription factor concentration serves as a signal inducing bifurcations and affecting delay effects on the system, with subcritical Hopf bifurcation occurring under small signal strength.
NONLINEAR DYNAMICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Fei Yu, Yuanshi Wang
Summary: This paper investigates an extended predator-prey model with the consideration that predators' fear reduces prey reproduction and the search speed of predators is influenced by prey density. The results show that high levels of fear can stabilize the coexistence steady state, while low levels lead to periodic oscillation. The analysis also reveals that a relatively small search speed of predators promotes the stability of the coexistence steady state, while a large speed results in periodic oscillation. Enhancing prey's sensitivity to predation risk or slowing the predator search speed can stabilize the coexistence steady state.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Zhizhi Wang, Bing Hu, Luyao Zhu, Jiahui Lin, Minbo Xu, Dingjiang Wang
Summary: In this paper, a cortex-basal ganglia resonance network is used to explore the mechanism of beta oscillation through Hopf bifurcation. The model includes a direct inhibitory projection from the subthalamic nucleus (STN) to the cortex excitatory nuclei (EXN), which is different from traditional views. The critical conditions of delay for oscillation and the effects of key parameters on Hopf bifurcation points are analyzed. The results reveal the importance of delay and the impact of different parameters on amplitude and frequency of oscillation.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Review
Neurosciences
Lingyun (Ivy) Xiong, Alan Garfinkel
Summary: This article argues that oscillations play critical physiological roles in avoiding desensitization, maintaining balanced chemical levels, increasing resistance to noise, reconciling incompatible conditions, and synchronizing small units into one large effect. It also emphasizes the importance of a dynamic approach and nonlinear dynamics in understanding and studying oscillatory processes in various levels of biological systems.
JOURNAL OF PHYSIOLOGY-LONDON
(2023)
Article
Mathematics, Applied
Abhijit Jana, Sankar Kumar Roy
Summary: This paper discusses the impact of environmental toxins on fisheries and proposes a toxicated intraguild fishery model to study the stability of coexistence equilibrium points and the occurrence of Hopf bifurcation. It also suggests a sustainable harvesting policy to maximize economic benefits. The proposed work is validated through numerical simulations, and some future research directions are provided.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Jyotirmoy Roy, Subrata Dey, Malay Banerjee
Summary: Discrete time delay is widely used in models of interacting populations to capture various biological processes. The primary goal of this article is to explore how delayed maturity in generalist predators qualitatively affects the dynamics of a predator-prey system. The analysis demonstrates that delayed maturation of generalist predators promotes stable coexistence.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics
Yuanxian Hui, Yunfeng Liu, Zhong Zhao
Summary: This paper investigates a delayed reaction-diffusion equation with carrying capacity-driven diffusion. The stability of the positive equilibrium solutions and the existence of the Hopf bifurcation are considered by studying the principal eigenvalue of an associated elliptic operator. The properties of the bifurcating periodic solutions are obtained using the normal form theory and the center manifold reduction. Numerical simulations are provided to illustrate the main theoretical results.
Article
Mathematics, Interdisciplinary Applications
Chunyan Gao, Fangqi Chen
Summary: In this study, a simple quorum sensing model was used to analyze the dynamical mechanisms in Pseudomonas aeruginosa. The optimal rate of model parameters for inducing oscillations without time delays was found to be crucial. Theoretical analysis and numerical simulation revealed that delays can induce subcritical Hopf bifurcation and oscillation hysteresis. The study also derived explicit formulas for stability and direction of periodic solutions bifurcating from Hopf bifurcations using center manifold and normal form theory. The results provide insights into the dynamics of quorum sensing system and have potential applications in bacterial drug delivery.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Biology
Bing Hu, Minbo Xu, Luyao Zhu, Jiahui Lin, Zhizhi Wang, Dingjiang Wang, Dongmei Zhang
Summary: In this paper, the oscillation mechanism in a computational model of Parkinson's disease was studied using bifurcation analysis and numerical simulation. The findings showed that abnormal coupling weights and delays can induce oscillatory activities. The study identified bidirectional Hopf bifurcations that can explain the oscillation mechanism in the model. Furthermore, it was observed that the effect of delay in inhibitory pathways is greater than that in excitatory pathways.
JOURNAL OF THEORETICAL BIOLOGY
(2022)
Article
Mathematics, Applied
Xiaoyan Hu, Bo Sang, Ning Wang
Summary: In this work, a five-parameter jerk system with a hyperbolic sine nonlinearity is analyzed. The symmetrical and asymmetrical cases are studied, and the bifurcations are determined using analytical methods. The discovery of chaotic motion mechanisms in jerk systems is the main contribution of this work. Circuit simulations are used to validate the numerical results.
Article
Mathematics, Interdisciplinary Applications
Alvaro G. Lopez
Summary: In this study, we analyze the dynamics of a damped harmonic oscillator with a time-delayed feedback potential that depends on the system's state. By considering small time-delays, we find that the oscillator can be equivalently described by a Lienard system, allowing us to predict the occurrence of the first Hopf bifurcation and the emergence of self-oscillatory motion. We investigate bifurcation diagrams for various parameter values and examine the existence of multistable domains. Additionally, we observe the presence of two coexisting stable limit cycles represented by distinct energy levels using the Lyapunov energy function. Further exploration of the parameter space reveals the existence of a superposition limit cycle that encompasses two degenerate coexisting limit cycles at the fundamental energy level. Moreover, we uncover a multiscale strange attractor displaying intrinsic and robust intermittency when the system is significantly driven away from equilibrium.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Gamaliel Ble, Claudia Isabel Guzman-Arellano, Ivan Loreto-Hernandez
Summary: The dynamics of an intraguild predation system were analyzed, showing conditions for coexistence, equilibrium points, and different limit sets for a wide range of functional responses. These results highlight the complex interactions within the system.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Multidisciplinary
Mrinmoy Sardar, Subhas Khajanchi, Santosh Biswas, Sayed F. Abdelwahab, Kottakkaran Sooppy Nisar
Summary: A conceptual mathematical model for tumor-immune interaction is proposed and analyzed, consisting of three coupled non-linear ODEs. The model can exhibit complicated dynamical behaviors and the study includes the qualitative properties, existence of solutions, and local stability analysis of biological feasible steady states. The presence of IL-2 can cause effector cells to regress the tumor cell population.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Computer Science, Interdisciplinary Applications
Xiang-Ping Yan, Cun-Hua Zhang
Summary: This article investigates a generalized Logistic reaction-diffusion population model with mixed instantaneous and delayed feedback control on a one-dimensional bounded spatial domain, providing insights on the existence of positive steady states, local asymptotic stability, and Hopf bifurcation. It is demonstrated that when delayed feedback dominates, the model may undergo forward Hopf bifurcation at the positive steady state, with bifurcating periodic solutions being locally orbitally asymptotically stable on the center manifold. Numerical simulations verify the reasonability of the main analytical conclusions.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Physics, Multidisciplinary
Qiubao Wang, Zhouyu Hu, Yanling Yang, Congqing Zhang, Zikun Han
Summary: This paper investigates the effects of different memory effects on the evolution of species population densities. A stochastic logistic model driven by non-Gaussian noise, with discrete and distributed time-delay, is considered. The results show a change in the population system from a single steady-state to a bi-periodic oscillation to a single steady-state again as memory intensity increased from weak to strong.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Binandita Barman, Bapan Ghosh
Summary: This paper examines a two-patch Rosenzweig-MacArthur predator-prey model with prey dispersal, finding that delayed prey dispersal can potentially alter the system's stability.
INTERNATIONAL JOURNAL OF MODELLING AND SIMULATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Angela da Silva, N. C. Pati, Paulo C. Rech
Summary: In this paper, a novel 3D autonomous nonlinear system with logarithmic nonlinearity is designed and explored. The system is constructed by replacing the variable y in the second equation of the Lorenz model with a nonlinear logarithmic term In |y|. The emergence of shrimp-shaped periodic structures in chaotic regime with period-adding phenomenon, and coexisting periodic-chaotic attractors, which are not found in the Lorenz model, are revealed. The stability, bifurcation patterns, and chaotic behaviors of the system, as well as the complexity of the basin sets for the coexisting attractors, are studied.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2022)
Article
Engineering, Multidisciplinary
Binandita Barman, Bapan Ghosh
Summary: This study proposes four predator-prey models and analyzes the effect of time delay on their stability. It was found that in models with intraspecific competition, the stable equilibrium may maintain its stability due to varying delay, and stability switching is impossible in all models.
INTERNATIONAL JOURNAL OF MODELLING AND SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Rajni, Bapan Ghosh
Summary: In this study, we investigate a discrete-time system based on the continuous-time Rosenzweig-MacArthur model. By varying the carrying capacity of the prey species and introducing prey and predator harvesting, we analyze the system's dynamics. Our results reveal complex behaviors such as multistability, chaos, and the paradox of enrichment. We also identify the hydra effect, a counter-intuitive phenomenon where predator biomass increases under predator mortality.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Bapan Ghosh, Suruchi Sarda, Shuchi Sahu
Summary: This paper analyzes a class of discrete-time delayed predator-prey models and explores the effects of time delay, carrying capacity, and harvesting on chaotic motion. A torus doubling route to chaos is discovered, which has been relatively less reported in existing literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Asep K. Supriatna, Hennie Husniah, Edy Soewono, Bapan Ghosh, Yedhi Purwanto, Elah Nurlaelah
Summary: This paper proposes and analyzes a mathematical model, in the form of a system of integral equations, for the transmission of dengue disease between human and mosquitoes. The study explores the effects of age-dependent functions and the presence of wolbachia infection on the dynamics of the disease. The results suggest that wolbachia infection has the potential to serve as a biological control agent for eliminating dengue in the human population.
Article
Mathematics, Interdisciplinary Applications
Shilpa Garai, N. C. Pati, Nikhil Pal, G. C. Layek
Summary: We report the existence of periodic and shrimp-shaped structures in the bi-parameter space of a predator-prey model. Our analysis of stability behaviors, bifurcations, and Lyapunov exponent shows complex dynamical behaviors and the emergence of a new type of periodic structure. Additionally, we observe the coexistence of three heterogeneous attractors and the presence of basin boundaries, indicating the unpredictability of the model. Our findings highlight the dependence of predator-prey oscillations on initial densities in certain parameter regions.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Bapan Ghosh, Binandita Barman, Manideepa Saha
Summary: This article presents a predator-prey model with dissimilar functional and numerical responses that induce an Allee effect and a time delay. By varying the time delay, the system exhibits four different dynamic behaviors, which is a novelty in a single population model with only one delay. The asymmetry in functional and numerical responses leads to the variation in dynamics. Stability theorems are provided and numerically verified. Additionally, new and interesting observations are made, including cases where the system remains unstable, stability changes, and instability switching occurs.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
N. C. Pati, Bapan Ghosh
Summary: In this study, we examine the effects of delayed harvesting on the stability of the predator-prey model. By analyzing the stability of the system in the effort-delay bi-parameter plane, we obtain novel dynamical scenarios and complex dynamics. It is discovered that delayed harvesting can destabilize the system and lead to effort-induced chaos via period-doubling mechanism, which does not occur in non-delayed harvesting.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Condensed Matter
N. C. Pati
Summary: We introduce a four-dimensional generalized Lorenz system to describe a rotating weakly shear-thinning fluid layer subjected to heating from below. We report on various bifurcation patterns leading to chaotic convection. The system exhibits coexisting multiple attractors with different heterogeneous combinations, including fixed point-periodic, multi-periodic with different periods, fixed point-chaotic, and periodic-chaotic, depending on initial conditions and system parameters. Smooth and fractal basin boundaries can occur in the basin of attraction corresponding to the coexisting attractors, and the uncertainty fractional method is employed to explore the fractality of the basin boundaries.
EUROPEAN PHYSICAL JOURNAL B
(2023)
Article
Engineering, Mechanical
N. C. Pati, Bapan Ghosh
Summary: The effects of time delay on the dynamics of a predator-prey system with multiple coexisting equilibria are investigated. The study reveals the presence of focus-node and cycle-node bistability in the absence of delay. The delay-induced stability and bifurcations of the coexisting equilibria, as well as the evolution of bistability, are analyzed. Criteria for different stability scenarios driven by delay are derived, and the control of bistability by delay through different bistable modes is demonstrated. Transition from bistable to monostable dynamics is found to occur through a homoclinic bifurcation. Furthermore, the impact of delay on the biological conservation of populations is assessed by computing mean density, showing both beneficial and harmful effects depending on bistability.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Vitaly Chernik, Pavel Buklemishev
Summary: The paper introduces a simple 2D model for describing the cell motility on a homogeneous isotropic surface. The model incorporates the dynamics of complex actomyosin liquid, which affects the boundary dynamics and cell motility. It consists of a system of equations with a free boundary domain and includes a non-local term. The numerical solution of this model is presented in this work.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Hasan Karjoun, Abdelaziz Beljadid
Summary: In this study, we developed a numerical model based on the depth-averaged shallow water equations to simulate flows through vegetation field. The model takes into account the drag and inertia forces induced by vegetation, using different formulations for the stem drag coefficient. Turbulence induced by vegetation is also considered through the addition of diffusion terms in the momentum equations. The proposed numerical model is validated through numerical simulations and shows good accuracy in simulating overland flows under vegetation effects.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Bechir Naffeti, Hamadi Ammar, Walid Ben Aribi
Summary: This paper proposes a branch and bound multidimensional Holder optimization method, which converts a multivariate objective function into a single variable function and minimizes it using an iterative optimization method. The method is applied to solve a parameters identification problem resulting from the increase in infections, providing information about the prevalence and infection force.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Heba F. Eid, Erik Cuevas, Romany F. Mansour
Summary: The proposed modified Bonobo optimizer algorithm dynamically adjusts the trajectory of each search agent to overcome the flaw of the original algorithm and improve the performance and solution quality by exploring and exploiting different regions of the solution space.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Farshid Mehrdoust, Idin Noorani, Juho Kanniainen
Summary: This paper proposes a Markov-switching model to evaluate the dynamics of commodity futures and spot prices, and introduces a hidden Markov chain to model the sudden jumps in commodity prices. The model is calibrated using the crude oil spot price and estimation-maximization algorithm. The study also evaluates European call options written on crude oil futures under the regime-switching model and derives Greek formulas for risk assessment. The importance of this paper is rated at 8 out of 10.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Rupa Mishra, Tapas Kumar Saha
Summary: This paper presents a control scheme for distributed generation units to operate in stand-alone and grid-connected modes, with a smooth transition between the two. The control strategy includes predictive control for voltage and frequency regulation in stand-alone mode, and power control for symmetrical and unbalanced grid voltage conditions in grid-connected mode. The proposed control method improves power factor, reduces grid current harmonics, and eliminates grid frequency ripple.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Yu Wang, Yang Tian, Yida Guo, Haoping Wang
Summary: This paper proposes a multi-level control strategy for lower limb patient-exoskeleton coupling system (LLPECS) in rehabilitation training based on active torque. The controller consists of three sub-controllers: gait adjustment layer, interaction torque design layer, and trajectory tracking layer. The effectiveness of the proposed control strategy is demonstrated through co-simulations in the SimMechanics environment using an exoskeleton virtual prototype developed in SolidWorks.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Takuji Arai, Yuto Imai
Summary: The Barndorff-Nielsen and Shephard model is a jump-type stochastic volatility model, and this paper proposes two simulation methods for computing option prices under a representative martingale measure. The performance of these methods is evaluated through numerical experiments.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Wanai Li
Summary: This paper proposes a new framework that combines quadrature-based and quadrature-free discontinuous Galerkin methods and applies them to triangular and tetrahedral grids. Four different DG schemes are derived by choosing specific test functions and collocation points, improving computational efficiency and ease of code implementation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiyuan Chen, Qiubao Wang
Summary: This paper introduces a technique that combines dynamical mechanisms and machine learning to reduce dimensionality in high-dimensional complex systems. The method utilizes Hopf bifurcation theory to establish a model paradigm and utilizes machine learning to train location parameters. The effectiveness and robustness of the proposed method are tested and validated through experiments and simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Muhammad Farman, Aqeel Ahmad, Anum Zehra, Kottakkaran Sooppy Nisar, Evren Hincal, Ali Akgul
Summary: Diabetes is a significant public health issue that affects millions of people worldwide. This study proposes a mathematical model to understand the mechanisms of glucose homeostasis, providing valuable insights for diabetes management. The model incorporates fractional operators and analyzes the impact of a new wave of dynamical transmission on equilibrium points, offering a comprehensive understanding of glucose homeostasis.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Gholamreza Shobeyri
Summary: This study introduces two improved Laplacian models for more accurate simulation of free surface flows in the context of the MPS method. The higher accuracy of these models compared to the traditional methods is verified through solving 2D Poisson equations and solving three benchmark free surface flow problems. These models can also resolve the issue of wave damping in the original MPS computations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Qiang Li, Jinling Liang, Weiqiang Gong, Kai Wang, Jinling Wang
Summary: This paper addresses the problem of nonfragile state estimation for semi-Markovian switching complex-valued networks with time-varying delay. By constructing an event-triggered generator and solving matrix inequalities, less conservative criteria are obtained, and the gains of the nonfragile estimator are explicitly designed. A numerical example is provided to demonstrate the effectiveness of the proposed estimation scheme.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Gengen Zhang, Jingyu Li, Qiong-Ao Huang
Summary: In this paper, a novel class of unconditionally energy stable schemes are constructed for solving gradient flow models by combining the relaxed scalar auxiliary variable (SAV) approach with the linear multistep technique. The proposed schemes achieve second-order temporal accuracy and strictly unconditional energy stability.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
S. Clain, J. Figueiredo
Summary: This study proposes a detailed construction of a very high-order polynomial representation and introduces a functional to assess the quality of the reconstruction. Several optimization techniques are implemented and their advantages in terms of accuracy and stability are demonstrated.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
