scholarly journals Modelling and Analysis of a Host-Parasitoid Impulsive Ecosystem under Resource Limitation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Peipei Wang ◽  
Wenjie Qin ◽  
Guangyao Tang
Keyword(s):  
Pest Control ◽  
Bifurcation Analysis ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Limited Resource ◽  
Optimal Number ◽  
Theoretical Development ◽  
Multiple Attractors ◽  
Pest Outbreaks ◽  
Impulsive Model

With a long history of theoretical development, biological model has focused on the interaction of a parasitoid and its host. In this paper, two Nicholson-Bailey models with a nonlinear pulse control strategy are proposed and analyzed to examine how limited resource affects the pest control. For a fixed-time discrete impulsive model, the existence and stability of the host-free periodic solution are derived. Threshold analysis suggests that it is critical to release parasitoid in an optimal number in case of the happening of the intra-specific competition, which will seriously affect the pest control. Bifurcation analysis reveals that the model exists complex dynamics including period doubling, chaotic solutions, coexistence of multiple attractors, and so on. For a state-dependent discrete impulsive model, the numerical simulations for bifurcation analysis are studied, the results show that how the key parameters and the initial densities of both populations affect the pest outbreaks, and consequently the relative biological implications with respect to pest control are discussed.

Complex Dynamics in a Memristive Diode Bridge-Based MLC Circuit: Coexisting Attractors and Double-Transient Chaos

2021 ◽  
Vol 31 (03) ◽  
pp. 2150049
Author(s):  
A. Chithra ◽  
T. Fonzin Fozin ◽  
K. Srinivasan ◽  
E. R. Mache Kengne ◽  
A. Tchagna Kouanou ◽  
...  
Keyword(s):  
Complex Dynamics ◽  
Basin Of Attraction ◽  
Period Doubling ◽  
Transient Chaos ◽  
Multiple Attractors ◽  
Simulation Tools ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Crisis Scenarios ◽  
Complex Phenomena

This paper uncovers some striking and new complex phenomena in a memristive diode bridge-based Murali–Lakshmanan–Chua (MLC) circuit. These striking dynamical behaviors include the coexistence of multiple attractors and double-transient chaos. Also, period-doubling, chaos, crisis scenarios are observed in the system when varying the amplitude of the external excitation. Numerical simulation tools like phase portrait, cross-section basin of attraction, Lyapunov spectrum, bifurcation diagrams and time series are used to highlight the complex dynamical behaviors in the memristive system. Further, practical realizations of the circuit both in PSpice and real-laboratory measurements match well with the observed numerical simulations.

scholarly journals Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenjie Qin ◽  
Guangyao Tang ◽  
Sanyi Tang
Keyword(s):  
Pest Control ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Limited Resource ◽  
Control Measures ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pest Outbreaks ◽  
Wide Range

A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.

Discrete Switching Host-Parasitoid Models with Integrated Pest Control

2014 ◽  
Vol 24 (09) ◽  
pp. 1450114 ◽  
Author(s):  
Changcheng Xiang ◽  
Zhongyi Xiang ◽  
Sanyi Tang ◽  
Jianhong Wu
Keyword(s):  
Pest Control ◽  
Complex Dynamics ◽  
Control Measures ◽  
Switching Frequency ◽  
Multiple Attractors ◽  
Multiple Control ◽  
Different Types ◽  
Existence And Stability ◽  
Numerical Bifurcation ◽  
Integrated Pest Control

The switched discrete host-parasitoid model concerning integrated pest management (IPM) has been proposed in the present work, and the economic threshold (ET) is chosen to guide the switches. That is, if the density of host (pest) population increases and exceeds the ET, then the biological and chemical tactics are applied together. Those multiple control measures are suspended once the density of host falls below the ET. Firstly, the existence and stability of several types of equilibria of switched system have been discussed briefly, and two- or three-parameter bifurcation diagrams reveal the regions of different types of equilibria including regular and virtual equilibria. Secondly, numerical bifurcation analyses show that the switched discrete system may have very complex dynamics including the co-existence of multiple attractors and switched-like behavior among attractors. Finally, we address how the key parameters and initial values of both host and parasitoid populations affect the host outbreaks, switching frequencies or mean switching frequency, and consequently the relative biological implications with respect to pest control are discussed.

BIFURCATIONS AND CHAOS IN CELLULAR NEURAL NETWORKS

2003 ◽  
Vol 12 (04) ◽  
pp. 417-433 ◽  
Author(s):  
M. BIEY ◽  
P. CHECCO ◽  
M. GILLI
Keyword(s):  
Neural Networks ◽  
Bifurcation Analysis ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
First Order ◽  
Stable Periodic ◽  
Torus Breakdown

The dynamic behavior of first-order autonomous space invariant cellular neural networks (CNNs) is investigated. It is shown that complex dynamics may occur in very simple CNN structures, described by two-dimensional templates that present only vertical and horizontal couplings. The bifurcation processes are analyzed through the computation of the limit cycle Floquet's multipliers, the evaluation of the Lyapunov exponents and of the signal spectra. As a main result a detailed and accurate two-dimensional bifurcation diagram is reported. The diagram allows one to distinguish several regions in the parameter space of a single CNN. They correspond to stable, periodic, quasi-periodic, and chaotic behavior, respectively. In particular it is shown that chaotic regions can be reached through two different routes: period doubling and torus breakdown. We remark that most practical CNN implementations exploit first order cells and space-invariant templates: so far only a few examples of complex dynamics and no complete bifurcation analysis have been presented for such networks.

scholarly journals Complex Dynamics of Discrete SEIS Models with Simple Demography

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Hui Cao ◽  
Yicang Zhou ◽  
Baojun Song
Keyword(s):  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Complex Dynamics ◽  
Treatment Strategies ◽  
Period Doubling ◽  
Demographic Factors ◽  
Multiple Attractors ◽  
Equilibrium Dynamics ◽  
Epidemiological Factors ◽  
Dynamical Behaviors

We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.

scholarly journals Chemical Control for Host-Parasitoid Model within the Parasitism Season and Its Complex Dynamics

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Tao Wang ◽  
Youtang Zhang
Keyword(s):  
Pest Control ◽  
Chemical Control ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Pesticide Application ◽  
Multiple Attractors ◽  
Threshold Conditions ◽  
Existence And Stability ◽  
Numerical Bifurcation ◽  
Type Ii Functional Response

In the present paper, we develop a host-parasitoid model with Holling type II functional response function and chemical control, which can be applied at any time of each parasitism season or pest generation, and focus on addressing the importance of the timing of application pesticide during the parasitism season or pest generation in successful pest control. Firstly, the existence and stability of both the host and parasitoid populations extinction equilibrium and parasitoid-free equilibrium have been investigated. Secondly, the effects of key parameters on the threshold conditions have been discussed in more detail, which shows the importance of pesticide application times on the pest control. Thirdly, the complex dynamics including multiple attractors coexistence, chaotic behavior, and initial sensitivity have been studied by using numerical bifurcation analyses. Finally, the uncertainty and sensitivity of all the parameters on the solutions of both the host and parasitoid populations are investigated, which can help us to determine the key parameters in designing the pest control strategy. The present research can help us to further understand the importance of timings of pesticide application in the pest control and to improve the classical chemical control and to make management decisions.

Asymmetry-Induced Dynamics for a Class of Diode-Based Chaotic Circuits: A Case Study

2020 ◽  
pp. 2150077 ◽  
Author(s):  
Léandre Kamdjeu Kengne ◽  
Jacques Kengne ◽  
Nicole Adelaïde Kengnou Telem ◽  
Justin Roger Mboupda Pone ◽  
Hervé Thierry Kamdem Tagne
Keyword(s):  
Complex Dynamics ◽  
Period Doubling ◽  
Multiple Attractors ◽  
Asymmetric Mode ◽  
Nonlinear Component ◽  
Realistic Situation ◽  
Coexistence Of Multiple Attractors ◽  
Chaotic Circuits ◽  
Route To Chaos ◽  
Antiparallel Diodes

We consider the modeling and asymmetry-induced dynamics for a class of chaotic circuits sharing the same feature of an antiparallel diodes pair as the nonlinear component. The simple autonomous jerk circuit of [J. Kengne, Z. T. Njitacke, A. N. Nguomkam, M. T. Fouodji and H. B. Fotsin, Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit, Int. J. Bifurcation Chaos Appl. Sci. Eng.26 (2016) 1650081] is used as the prototype. In contrast to current approaches where the diodes are assumed to be identical (and thus a perfect symmetric circuit), we examine the more realistic situation where the diodes have different electrical properties in spite of unavoidable scattering of parameters. In this case, the nonlinear component formed by the diodes pair displays an asymmetric current–voltage characteristic which induces asymmetry of the whole circuit. The model is described by a continuous-time 3D autonomous system (ODEs) with exponential nonlinearities. We examine the chaos mechanism with respect to system parameters both in the symmetric and asymmetric modes of operation by using bifurcation diagrams and phase space trajectory plots as the main indicators. Period doubling route to chaos, merging crisis, and multiple coexisting (i.e., two, four, or six) mutually symmetric attractors are reported in the symmetric mode of oscillation. In the asymmetric mode, several unusual nonlinear behaviors arise such as coexisting bifurcations, hysteresis, asymmetric double-band chaotic attractor, crisis, and coexisting multiple (i.e., two, three, four, or five) asymmetric attractors for some suitable ranges of parameters. Theoretical analyses and circuit experiments show a very good agreement. The results obtained in this work let us conjecture that chaotic circuits with antiparallel diodes pair are capable of much more complex dynamics than what is reported in the current literature and thus should be reconsidered accordingly in spite of the approach followed in this work.

scholarly journals ANALYSIS OF BIFURCATIONS IN A POWER SYSTEM MODEL WITH EXCITATION LIMITS

2001 ◽  
Vol 11 (09) ◽  
pp. 2509-2516 ◽  
Author(s):  
RAJESH G. KAVASSERI ◽  
K. R. PADIYAR
Keyword(s):  
Power System ◽  
Bifurcation Analysis ◽  
Smooth Function ◽  
Period Doubling ◽  
System Model ◽  
System Behavior ◽  
Multiple Attractors ◽  
Period Doubling Bifurcations ◽  
Power System Model ◽  
Qualitative Changes

This paper studies bifurcations in a three node power system when excitation limits are considered. This is done by approximating the limiter by a smooth function to facilitate bifurcation analysis. Spectacular qualitative changes in the system behavior induced by the limiter are illustrated by two case studies. Period doubling bifurcations and multiple attractors are shown to result due to the limiter. Detailed numerical simulations are presented to verify the results and illustrate the nature of the attractors and solutions involved.

scholarly journals Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Changtong Li ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Period Doubling ◽  
Dynamical Behaviour ◽  
Period Doubling Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model

Abstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies.

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