scholarly journals Preventing extinction in Rastrelliger brachysoma using an impulsive mathematical model

2021 ◽  
Vol 7 (1) ◽  
pp. 1-24
Author(s):  
Din Prathumwan ◽  
◽  
Kamonchat Trachoo ◽  
Wasan Maiaugree ◽  
Inthira Chaiya ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Population Density ◽  
Upper Bound ◽  
Existence And Uniqueness ◽  
Periodic Behavior ◽  
Toxic Environment ◽  
Pacific Mackerel ◽  
The Stability ◽  
Theoretical Results

<abstract><p>In this paper, we proposed a mathematical model of the population density of Indo-Pacific mackerel (<italic>Rastrelliger brachysoma</italic>) and the population density of small fishes based on the impulsive fishery. The model also considers the effects of the toxic environment that is the major problem in the water. The developed impulsive mathematical model was analyzed theoretically in terms of existence and uniqueness, positivity, and upper bound of the solution. The obtained solution has a periodic behavior that is suitable for the fishery. Moreover, the stability, permanence, and positive of the periodic solution are investigated. Then, we obtain the parameter conditions of the model for which Indo-Pacific mackerel conservation might be expected. Numerical results were also investigated to confirm our theoretical results. The results represent the periodic behavior of the population density of the Indo-Pacific mackerel and small fishes. The outcomes showed that the duration and quantity of fisheries were the keys to prevent the extinction of Indo-Pacific mackerel.</p></abstract>

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals General fractional financial models of awareness with Caputo–Fabrizio derivative

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097552
Author(s):  
Amr MS Mahdy ◽  
Yasser Abd Elaziz Amer ◽  
Mohamed S Mohamed ◽  
Eslam Sobhy
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Numerical Simulations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Whole Number ◽  
Fractional System ◽  
Set Up ◽  
Theoretical Results

A Caputo–Fabrizio (CF) form a fractional-system mathematical model for the fractional financial models of awareness is suggested. The fundamental attributes of the model are explored. The existence and uniqueness of the suggest fractional financial models of awareness solutions are given through the fixed point hypothesis. The non-number request subordinate gives progressively adaptable and more profound data about the multifaceted nature of the elements of the proposed partial budgetary models of mindfulness model than the whole number request models set up previously. In order to confirm the theoretical results and numerical simulations studies with Caputo derivative are offered.

scholarly journals A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

2020 ◽  
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

scholarly journals A stochastic mathematical model of two different infectious epidemic under vertical transmission

2021 ◽  
Vol 19 (3) ◽  
pp. 2179-2192
Author(s):  
Xunyang Wang ◽  
◽  
Canyun Huang ◽  
Yixin Hao ◽  
Qihong Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Vertical Transmission ◽  
Biological Significance ◽  
Sufficient Conditions ◽  
Discussion Section ◽  
Stochastic Permanence ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Well Posed ◽  
Theoretical Results

<abstract><p>In this study, considering the effect of environment perturbation which is usually embodied by the alteration of contact infection rate, we formulate a stochastic epidemic mathematical model in which two different kinds of infectious diseases that spread simultaneously through both horizontal and vertical transmission are described. To indicate our model is well-posed and of biological significance, we prove the existence and uniqueness of positive solution at the beginning. By constructing suitable $ Lyapunov $ functions (which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation) and applying $ It\hat{o} $'s formula as well as $ Chebyshev $'s inequality, we also establish the sufficient conditions for stochastic ultimate boundedness. Furthermore, when some main parameters and all the stochastically perturbed intensities satisfy a certain relationship, we finally prove the stochastic permanence. Our results show that the perturbed intensities should be no greater than a certain positive number which is up-bounded by some parameters in the system, otherwise, the system will be surely extinct. The reliability of theoretical results are further illustrated by numerical simulations. Finally, in the discussion section, we put forward two important and interesting questions left for further investigation.</p></abstract>

Study on the Response of Flexible Joint Coupled With Unbalanced Rotor

2005 ◽  
Author(s):  
Zhen-Zhong Zhang ◽  
Cun-Sheng Zhao ◽  
Shi-Jian Zhu
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Dynamic Response ◽  
Periodic Coefficient ◽  
Steady Solution ◽  
Stability Conditions ◽  
Flexible Joint ◽  
Unbalanced Rotor ◽  
The Stability ◽  
The Mathematical Model

The dynamic response of the flexible joint with unbalanced rotor was analyzed. The mathematical model was investigated and simplified and the unbalanced system was found to be with periodic coefficient. The stability conditions of the periodic solution were simply derived from existing conclusions. And a method for an approximate steady solution was presented. The validity was confirmed by the simulation.

scholarly journals Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1291
Author(s):  
Jie Pan ◽  
Lianglin Xiong
Keyword(s):  
Neural Networks ◽  
Existence And Uniqueness ◽  
Variable Coefficient ◽  
Matrix Theory ◽  
Computing Complexity ◽  
Derivative Formula ◽  
Inequality Techniques ◽  
The Fixed Point Theorem ◽  
The Stability ◽  
Theoretical Results

In this paper, we fixate on the stability of varying-time delayed memristive quaternionic neural networks (MQNNs). With the help of the closure of the convex hull of a set the theory of differential inclusion, MQNN are transformed into variable coefficient continuous quaternionic neural networks (QNNs). The existence and uniqueness of the equilibrium solution (ES) for MQNN are concluded by exploiting the fixed-point theorem. Then a derivative formula of the quaternionic function’s norm is received. By utilizing the formula, the M-matrix theory, and the inequality techniques, some algebraic standards are gained to affirm the global exponential stability (GES) of the ES for the MQNN. Notably, compared to the existing work on QNN, our direct quaternionic method operates QNN as a whole and markedly reduces computing complexity and the gained results are more apt to be verified. The two numerical simulation instances are provided to evidence the merits of the theoretical results.

scholarly journals A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 376
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Stability and Neimark-Sacker Bifurcation Analysis in a Genetic Network with Delay

2017 ◽  
Vol 21 (2) ◽  
pp. 278-283
Author(s):  
Feng Liu ◽  
◽  
Xiang Yin ◽  
Zhe Zhang ◽  
Fenglan Sun ◽  
...  
Keyword(s):  
Periodic Solution ◽  
Normal Form ◽  
Center Manifold ◽  
Genetic Model ◽  
Genetic Network ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
The Stability ◽  
Theoretical Results

This paper investigates a genetic model with delay. The stability, direction, and bifurcation periodic solution is derived by using the center manifold theorem and normal form theory. Numerical simulations illustrate the theoretical results.

scholarly journals Correlated Stochastic Epidemic Model for the Dynamics of SARS-CoV-2 with Vaccination

2021 ◽  
Author(s):  
Tahir Khan ◽  
Roman Ullah ◽  
Gul Zaman ◽  
Youssef Khatib
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Human Population ◽  
Sufficient Conditions ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
Virus Spreading ◽  
Theoretical Results

Abstract We formulate a mathematical model has been proposed to describe the stochastic influence of SARS-CoV-2 virus with various sources of randomness and vaccination. We assume the various sources of ran-domness in each population groups by different Brownian motion. We develop the correlated stochastic model by taking into account the various sources of randomness by different Brownian motions and distributed the total human population in three groups of susceptible, infected and recovered with reservoir class. Because reservoir play a significant role in the transmission of SARS-CoV-2 virus spreading. Moreover, the vaccination of susceptible are also accorded. Once we formulate the correlated stochastic model, the existence and uniqueness of positive solution will be discussed to show the problem feasibility. The SARS-CoV-2 extinction as well as persistency will be also discussed and we will obtain the sufficient conditions for it. At the last all the theoretical results will be supported via numerical/graphical findings.

Global dynamics of delayed intraguild predation model with intraspecific competition

2018 ◽  
Vol 11 (08) ◽  
pp. 1850116
Author(s):  
Zhenzhen Li ◽  
Binxiang Dai
Keyword(s):  
Periodic Solution ◽  
Global Existence ◽  
Intraspecific Competition ◽  
Intraguild Predation ◽  
Critical Value ◽  
Existence Results ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
The Stability ◽  
Theoretical Results

A delayed intraguild predation (IGP) model with intraspecific competition is considered. It is shown that the delay has a destabilizing effect and induces oscillations. The global existence results of periodic solutions bifurcating from the positive equilibrium are established. It is shown that there exists at least one nontrival periodic solution when the delay passes through a certain critical value. Numerical simulations are performed to illustrate our theoretical results and show that intraspecific competition can also affect the stability of the positive equilibrium of the system.

Sign in / Sign up

Export Citation Format

Share Document