scholarly journals Host-Parasitoid Model With Intraspecific Competitions

2012 ◽  
Vol 1 (2) ◽  
pp. 105
Author(s):  
Banshidhar Sahoo ◽  
Swarup Poria
Keyword(s):  
Discrete Time ◽  
Bifurcation Analysis ◽  
Complex Dynamics ◽  
Handling Time ◽  
Phase Portraits ◽  
Search Rate ◽  
Reasonable Range ◽  
Different Types ◽  
Oscillatory Coexistence ◽  
Parameter Values

In this paper a discrete-time host-parasitoid model with intraspecific competitions is proposed. Phase portraits are drawn for different types of intraspecific competitions to notice the effects of intraspecific competitions for biologically reasonable range of parameter values. Bifurcation analysis is done with respect to instantaneous search rate as well as handling time for different types of intraspecific competitions. Many forms of complex dynamics such as chaos, periodic windows etc. are observed. The stable coexistence as well as oscillatory coexistence of host and parasitoid are shown under different types of intraspecific competitions. The Hopf point and attractor crises exist for different intraspecific competitions.

scholarly journals Dynamical phenomena induced by bottleneck

2010 ◽  
Vol 368 (1928) ◽  
pp. 4543-4562 ◽  
Author(s):  
I. Gasser ◽  
B. Werner
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Bifurcation Analysis ◽  
Complex Dynamics ◽  
Standing Waves ◽  
Continuation Methods ◽  
Traffic Dynamics ◽  
Poincaré Maps ◽  
Different Types ◽  
The Way

We study a microscopic follow-the-leader model on a circle of length L with a bottleneck. Allowing large bottleneck strengths we encounter very interesting traffic dynamics. Different types of waves—travelling and standing waves and combinations of both wave types—are observed. The way to find these phenomena requires a good understanding of the complex dynamics of the underlying (nonlinear) equations. Some of the phenomena, like the ponies-on-a-merry-go-round solutions, are mathematically well known from completely different applications. Mathematically speaking we use Poincaré maps, bifurcation analysis and continuation methods beside numerical simulations.

scholarly journals Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Chengmin Hou ◽  
Sui Sun Cheng
Keyword(s):  
Control System ◽  
Discrete Time ◽  
Bifurcation Analysis ◽  
Control Model ◽  
Threshold Parameter ◽  
State Variable ◽  
Periodic Model ◽  
Different Types ◽  
Bang Bang Control ◽  
Time Periodic

A discrete-time periodic model with bang-bang feedback control is investigated. It is shown that each solution tends to one of four different types of limit 2-cycles. Furthermore, the accompanying initial regions for each type of solutions can be determined. When a threshold parameter is introduced in the bang-bang function, our results form a complete bifurcation analysis of our control model. Hence, our model can be used in the design of a control system where the state variable fluctuates between two state values with decaying perturbation.

scholarly journals Bifurcation analysis and chaos control in discrete-time modified Leslie–Gower prey harvesting model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Bilal Ajaz ◽  
Umer Saeed ◽  
Qamar Din ◽  
Irfan Ali ◽  
Muhammad Israr Siddiqui
Keyword(s):  
Discrete Time ◽  
Bifurcation Analysis ◽  
Chaos Control

Symmetry-breaking bifurcations in resonant surface waves

1989 ◽  
Vol 199 ◽  
pp. 495-518 ◽  
Author(s):  
Z. C. Feng ◽  
P. R. Sethna
Keyword(s):  
Normal Form ◽  
Symmetry Breaking ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Internal Resonance ◽  
Travelling Waves ◽  
Chaotic Behaviour ◽  
Derived Set ◽  
Parameter Values ◽  
Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

Intervention Time in Target-Oriented Chaos Control

2021 ◽  
Vol 31 (09) ◽  
pp. 2150134
Author(s):  
Juan Segura
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Single Species ◽  
Positive Equilibrium ◽  
Population Stability ◽  
Determine Parameter ◽  
And Control ◽  
Parameter Values ◽  
Proportional Feedback

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

Hypernetwork models based on random hypergraphs

2019 ◽  
Vol 30 (08) ◽  
pp. 1950052
Author(s):  
Feng Hu ◽  
Jin-Li Guo ◽  
Fa-Xu Li ◽  
Hai-Xing Zhao
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
World Systems ◽  
Uniform Hypergraphs ◽  
Different Types ◽  
Powerful Means ◽  
Simulation Results ◽  
Parameter Values ◽  
Random Hypergraphs

Hypernetworks are ubiquitous in real-world systems. They provide a powerful means of accurately depicting networks of different types of entity and will attract more attention from researchers in the future. Most previous hypernetwork research has been focused on the application and modeling of uniform hypernetworks, which are based on uniform hypergraphs. However, random hypernetworks are generally more common, therefore, it is useful to investigate the evolution mechanisms of random hypernetworks. In this paper, we construct three dynamic evolutional models of hypernetworks, namely the equal-probability random hypernetwork model, the Poisson-probability random hypernetwork model and the certain-probability random hypernetwork model. Furthermore, we analyze the hyperdegree distributions of the three models with mean-field theory, and we simulate each model numerically with different parameter values. The simulation results agree well with the results of our theoretical analysis, and the findings indicate that our models could help understand the structure and evolution mechanisms of real systems.

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