scholarly journals Dynamical Properties of a Herbivore-Plankton Impulsive Semidynamic System with Eating Behavior

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yufei Wang ◽  
Huidong Cheng ◽  
Qingjian Li
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Detailed Analysis ◽  
Eating Behavior ◽  
Poincaré Map ◽  
Effective Control ◽  
Poincare Map ◽  
Phase Concentration ◽  
Dynamical Properties ◽  
The Relationship

In this paper, an impulsive semidynamic system of the relationship between plankton and herbivore is established, and the Poincaré map method is used to extend the new properties of the model. We define the Poincaré map of the impulsive point series in phase concentration and analyze the characteristics. A comprehensive and detailed analysis of the periodic solution is performed. In addition, the numerical simulations illustrate the correctness of our arguments. The results show that plankton and herbivore can survive stably under effective control.

scholarly journals Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zhenzhen Shi ◽  
Qingjian Li ◽  
Weiming Li ◽  
Huidong Cheng
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Poincaré Map ◽  
Global Dynamics ◽  
Poincare Map ◽  
Existence And Stability ◽  
Sufficient And Necessary Conditions ◽  
Predator Model ◽  
Order One Periodic Solution

An integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincaré map which is defined on the phase set and discuss its main properties including monotonicity, continuity, and discontinuity. Secondly, the existence and stability of the boundary order-one periodic solution are proved by the method of Poincaré map. According to the Poincaré map and related differential equation theory, the conditions of the existence and global stability of the order-one periodic solution are obtained when ΦyA<yA, and we prove the sufficient and necessary conditions for the global asymptotic stability of the order-one periodic solution when ΦyA>yA. Furthermore, we prove the existence of the order-kk≥2 periodic solution under certain conditions. Finally, we verify the main results by numerical simulation.

EFFECTIVE COMPUTATION OF THE POINCARÉ MAP FOR THE ANALYSIS OF NONLINEAR DYNAMIC CIRCUITS/SYSTEMS USING RUNGE-KUTTA TRIPLES

1994 ◽  
Vol 04 (01) ◽  
pp. 93-98 ◽  
Author(s):  
L. FINGER ◽  
H. UHLMANN
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Dynamic ◽  
Poincaré Map ◽  
Global Analysis ◽  
Interpolation Polynomial ◽  
Poincare Map ◽  
Dynamic Circuits ◽  
Dense Output ◽  
Computer Aided ◽  
Runge Kutta

An enhancement of the classical Runge—Kutta technique for numerical simulations is presented for the computer-aided global analysis of nonlinear dynamic circuits/systems. With Runge—Kutta triples a remarkable saving of calculation time can be achieved by using an interpolation polynomial for dense output. The Runge—Kutta triples are applied to calculate the Poincaré map for autonomous models/systems.

Symmetry Breaking and Symmetry Increasing in a Vibro-Impact with Symmetric Two-Sided Constraints

2011 ◽  
Vol 66-68 ◽  
pp. 229-234
Author(s):  
Yuan Yue ◽  
Jian Huab Xie
Keyword(s):  
Fixed Point ◽  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Poincaré Map ◽  
Jacobi Matrix ◽  
Degree Of Freedom ◽  
Poincare Map ◽  
Impact System ◽  
Existence Conditions ◽  
Three Degree Of Freedom

A three-degree-of-freedom vibro-impact system with symmetric two-sided constraints is considered. Existence conditions of the symmetric period -2 motion are given, and the symmetric period n-2 motion of the system is deduced analytically. The six dimensional Poincaré map is established, and the Jacobi matrix of the symmetrixc fixed point is obtained. By the numerical simulations, we show that symmetry breaking and symmetry increasing exists in the vibro-impact system with symmetric two-sided constraints.

scholarly journals Dynamic Complexity of a Phytoplankton-Fish Model with the Impulsive Feedback Control by means of Poincaré Map

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Dezhao Li ◽  
Yu Liu ◽  
Huidong Cheng
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Poincaré Map ◽  
Dynamic Change ◽  
Sufficient Conditions ◽  
Reference Value ◽  
Poincare Map ◽  
Dynamic Complexity ◽  
Fish Model ◽  
Necessary And Sufficient

The phytoplankton-fish model for catching fish with impulsive feedback control is established in this paper. Firstly, the Poincaré map for the phytoplankton-fish model is defined, and the properties of monotonicity, continuity, differentiability, and fixed point of Poincaré map are analyzed. In particular, the continuous and discontinuous properties of Poincaré map under different conditions are discussed. Secondly, we conduct the analysis of the necessary and sufficient conditions for the existence, uniqueness, and global stability of the order-1 periodic solution of the phytoplankton-fish model and obtain the sufficient conditions for the existence of the order-kk≥2 periodic solution of the system. Numerical simulation shows the correctness of our results which show that phytoplankton and fish with the impulsive feedback control can live stably under certain conditions, and the results have certain reference value for the dynamic change of phytoplankton in aquatic ecosystems.

scholarly journals Dynamic Analysis of a Plankton-Herbivore State-Dependent Impulsive Model With Action Threshold Depending On The Density and Its Changing Rate

2021 ◽  
Author(s):  
Wei Li ◽  
Tonghua Zhang ◽  
Yufei Wang ◽  
Huidong Cheng
Keyword(s):  
Periodic Solution ◽  
Poincaré Map ◽  
Complex Dynamics ◽  
Economic Benefits ◽  
Rate Of Change ◽  
Poincare Map ◽  
The Sustainable Development ◽  
State Dependent ◽  
Action Threshold ◽  
Impulsive Model

Abstract A plankton-herbivore state-dependent impulsive model with nonlinear impulsive functions and action threshold including population density and rate of change is proposed. Since the use of action threshold makes the model have complex phase set and pulse set, we adopt the Poincaré map as a tool to study its complex dynamics. The Poincaré map is defined on the phase set and its properties in different situations are analyzed. Furthermore, the periodic solution of model are discussed, including the existence and stability conditions of the order-1 periodic solution and the existence of the order-k (k ≥ 2) periodic solutions. Compared with the fixed threshold in the existing literature, our results show that the use of action threshold is more practical, which is conducive to the sustainable development of population and makes people obtain more economic benefits. The analysis method used in this paper can study the complex dynamics of the model more comprehensively and deeply.

Periodic Solution Bifurcation and Spiking Dynamics of Impacting Predator–Prey Dynamical Model

2018 ◽  
Vol 28 (12) ◽  
pp. 1850147 ◽  
Author(s):  
Sanyi Tang ◽  
Xuewen Tan ◽  
Jin Yang ◽  
Juhua Liang
Keyword(s):  
Periodic Solution ◽  
Poincaré Map ◽  
Complex Dynamics ◽  
Poincare Map ◽  
Predator Prey ◽  
Threshold Conditions ◽  
Existence And Stability ◽  
The Stability ◽  
Nonmonotonic Functional Response ◽  
Solution Bifurcation

A planar predator–prey impacting system model with a nonmonotonic functional response function is proposed and analyzed. The existence and stability of a boundary order-1 periodic solution were investigated and the threshold conditions for a transcritical bifurcation and stable switching were obtained, and also the definition and properties of the Poincaré map are discussed. The main results indicate that multiple discontinuous points of the Poincaré map could induce the coexistence of multiple order-1 periodic solutions. Numerical analyses reveal the complex dynamics of the model including periodic adding and halving bifurcations, which could result in multiple active phases, among them rapid spiking and quiescence phases which can switch from one to another and consequently create complex bursting patterns. The main results reveal that it is beneficial to restore the stability and balance of a ecosystem for species with group defence by moderately reducing population densities and the group defence capacity.

Eating Behavior of Brazilian College Students: Influences of Lifestyle, Negative Affectivity, and Personal Characteristics

2020 ◽  
pp. 003151252098308
Author(s):  
Bianca G. Martins ◽  
Wanderson R. da Silva ◽  
João Marôco ◽  
Juliana A. D. B. Campos
Keyword(s):  
College Students ◽  
Eating Behavior ◽  
Emotional Eating ◽  
Eating Behaviors ◽  
Structural Model ◽  
Negative Affectivity ◽  
Personal Characteristics ◽  
Second Order ◽  
The Impact ◽  
The Relationship

In this study we proposed to estimate the impact of lifestyle, negative affectivity, and college students’ personal characteristics on eating behavior. We aimed to verify that negative affectivity moderates the relationship between lifestyle and eating behavior. We assessed eating behaviors of cognitive restraint (CR), uncontrolled eating (UE), and emotional eating (EE)) with the Three-Factor Eating Questionnaire-18. We assessed lifestyle with the Individual Lifestyle Profile, and we assessed negative affectivity with the Depression, Anxiety and Stress Scale-21. We constructed and tested (at p < .05) a hypothetical causal structural model that considered global (second-order) and specific (first-order) lifestyle components, negative affectivity and sample characteristics for each eating behavior dimension. Participants were 1,109 college students ( M age = 20.9, SD = 2.7 years; 65.7% females). We found significant impacts of lifestyle second-order components on negative affectivity (β = −0.57–0.19; p < 0.001–0.01) in all models. Physical and psychological lifestyle components impacted directly only on CR (β=−0.32–0.81; p < 0.001). Negative affectivity impacted UE and EE (β = 0.23–0.30; p < 0.001). For global models, we found no mediation pathways between lifestyle and CR or UE. For specific models, negative affectivity was a mediator between stress management and UE (β=−0.07; p < 0.001). Negative affectivity also mediated the relationship between thoughts of dropping an undergraduate course and UE and EE (β = 0.06–0.08; p < 0.001). Participant sex and weight impacted all eating behavior dimensions (β = 0.08–0.34; p < 0.001–0.01). Age was significant for UE and EE (β=−0,14– −0.09; p < 0.001–0.01). Economic stratum influenced only CR (β = 0.08; p = 0.01). In sum, participants’ lifestyle, negative emotions and personal characteristics were all relevant for eating behavior assessment.

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