Dynamical behaviors for generalized pendulum type equations with p-Laplacian

2020 ◽  
Vol 15 (5) ◽  
pp. 959-984
Author(s):  
Yanmin Niu ◽  
Xiong Li
Keyword(s):  
Dynamical Behaviors ◽  
Pendulum Type Equations

scholarly journals Complex Dynamical Behaviors of a Mixed Duopoly Game Based on Intellectual Property Rights Protection

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tong Chu ◽  
Yu Yu ◽  
Xiaoxue Wang
Keyword(s):  
Intellectual Property ◽  
Property Rights ◽  
Intellectual Property Rights ◽  
Mixed Duopoly ◽  
Fractal Structures ◽  
Rights Protection ◽  
Intellectual Property Rights Protection ◽  
Dynamical Behaviors ◽  
Property Rights Protection ◽  
Coexistence Of Attractors

Based on the oligopoly game theory and the intellectual property rights protection policy, we investigate the complex dynamical behaviors of a mixed duopoly game with quadratic cost. In the new system, a few parameters are improved by considering intellectual property rights protection and the stability conditions of the Nash equilibrium point are discussed in detail. A set of the two-dimensional bifurcation diagrams is demonstrated by using numerical modeling, and these diagrams show abundant complex dynamical behaviors, such as coexistence of attractors, different bifurcation, and fractal structures. These dynamical properties can present the long-run effects of strengthening intellectual property protection.

The role of shearing effect in evolution of the microscopic behavior of wax crystals

2021 ◽  
Author(s):  
Yuanhao Li ◽  
Jian Zhao ◽  
Hang Dong ◽  
Xiangrui Xi
Keyword(s):  
Crude Oil ◽  
Waxy Crude Oil ◽  
Waxy Crude ◽  
Dynamical Behaviors ◽  
Physical Phenomena ◽  
Wax Crystals

The microstructure and dynamical behaviors of wax crystals in waxy crude oil are the fundamental reasons for a series of physical phenomena in the process of transportation. In order to...

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

scholarly journals Pharmacokinetic modeling of Gadolinium nanoparticles (Gd-NPs) with the sojourn time in vasa vasorum for the contrast enhanced MRI

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Angkhana Prommarat ◽  
Farida Chamchod
Keyword(s):  
Sojourn Time ◽  
Vasa Vasorum ◽  
Peripheral Arteries ◽  
Resonance Imaging ◽  
Differential Model ◽  
Transfer Rates ◽  
Dynamical Behaviors ◽  
Contrast Enhanced ◽  
Delay Differential

AbstractDeposition of lipid in the artery wall called atherosclerosis is recognized as a major cause of cardiovascular disease that leads to death worldwide. A better understanding into factors that may influence the delivery of gadolinium nanoparticles (Gd-NPs) that enhances quality of magnetic resonance imaging in diagnosis may provide a vital key for atherosclerotic treatment. In this study, we propose a delay differential model for describing the dynamics of Gd-NPs in bloodstream, peripheral arteries, and vasa vasorum with two phenomena of Gd-NPs during a sojourn in vasa vasorum. We then investigate the dynamical behaviors of Gd-NPs and explore the effects of sojourn time and transfer rates of Gd-NPs on the concentration of Gd-NPs in vasa vasorum at the 12th hour after the administration of gadolinium chelates contrast media and also the maximum concentration of Gd-NPs in peripheral arteries and vasa vasorum. Our results suggest that the sojourn of Gd-NPs in vasa vasorum may lead to complex behaviors of Gd-NPs dynamics, and transfer rates of Gd-NPs may have a significant impact on the concentration of Gd-NPs.

Dynamical Analysis of bantam-Regulated Drosophila Circadian Rhythm Model

2014 ◽  
Vol 24 (12) ◽  
pp. 1450161 ◽  
Author(s):  
Ying Li ◽  
Zengrong Liu
Keyword(s):  
Circadian Rhythm ◽  
Crucial Role ◽  
Target Genes ◽  
Classical Model ◽  
Dynamical Analysis ◽  
Biological Processes ◽  
Biological Mechanisms ◽  
Environmental Perturbations ◽  
Dynamical Behaviors ◽  
Important Regulator

MicroRNAs (miRNAs) interact with 3′untranslated region (UTR) elements of target genes to regulate mRNA stability or translation, and play a crucial role in regulating many different biological processes. bantam, a conserved miRNA, is involved in several functions, such as regulating Drosophila growth and circadian rhythm. Recently, it has been discovered that bantam plays a crucial role in the core circadian pacemaker. In this paper, based on experimental observations, a detailed dynamical model of bantam-regulated circadian clock system is developed to show the post-transcriptional behaviors in the modulation of Drosophila circadian rhythm, in which the regulation of bantam is incorporated into a classical model. The dynamical behaviors of the model are consistent with the experimental observations, which shows that bantam is an important regulator of Drosophila circadian rhythm. The sensitivity analysis of parameters demonstrates that with the regulation of bantam the system is more sensitive to perturbations, indicating that bantam regulation makes it easier for the organism to modulate its period against the environmental perturbations. The effectiveness in rescuing locomotor activity rhythms of mutated flies shows that bantam is necessary for strong and sustained rhythms. In addition, the biological mechanisms of bantam regulation are analyzed, which may help us more clearly understand Drosophila circadian rhythm regulated by other miRNAs.

Dynamical behaviors of the periodic parameter-switching system

2013 ◽  
Vol 73 (1-2) ◽  
pp. 29-37 ◽  
Author(s):  
Chun Zhang ◽  
Xiujing Han ◽  
Qinsheng Bi
Keyword(s):  
Switching System ◽  
Dynamical Behaviors ◽  
Parameter Switching

scholarly journals MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

2012 ◽  
Vol 09 ◽  
pp. 334-340 ◽  
Author(s):  
MADA SANJAYA WS ◽  
ISMAIL BIN MOHD ◽  
MUSTAFA MAMAT ◽  
ZABIDIN SALLEH
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Food Chain ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Bifurcation Points ◽  
Dynamical Behaviors ◽  
Practical Life ◽  
Parameter Values ◽  
Chain Interaction

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

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