Parametric stability and complex dynamical behavior of functionally graded rectangular thin plates subjected to in-plane inertial disturbance

2020 ◽  
Vol 234 ◽  
pp. 111728
Author(s):  
Chang-Cheng Du ◽  
Ying-Hui Li
Keyword(s):  
Dynamical Behavior ◽  
Functionally Graded ◽  
Thin Plates ◽  
Parametric Stability ◽  
Complex Dynamical Behavior

scholarly journals Complex Dynamical Behavior of a Predator-Prey System with Group Defense

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jianglin Zhao ◽  
Min Zhao ◽  
Hengguo Yu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Basis ◽  
Dynamical Behavior ◽  
Turing Instability ◽  
Equilibrium Density ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Group Defense ◽  
Complex Dynamical Behavior

A diffusive predator-prey system with prey refuge is studied analytically and numerically. The Turing bifurcation is analyzed in detail, which in turn provides a theoretical basis for the numerical simulation. The influence of prey refuge and group defense on the equilibrium density and patterns of species under the condition of Turing instability is explored by numerical simulations, and this shows that the prey refuge and group defense have an important effect on the equilibrium density and patterns of species. Moreover, it can be obtained that the distributions of species are more sensitive to group defense than prey refuge. These results are expected to be of significance in exploration for the spatiotemporal dynamics of ecosystems.

Density-Dependent Population Growth

2020 ◽  
pp. 29-46
Author(s):  
Michael J. Fogarty ◽  
Jeremy S. Collie
Keyword(s):  
Population Density ◽  
Population Growth ◽  
Density Dependence ◽  
Multiple Equilibria ◽  
Dynamical Behavior ◽  
Logistic Growth ◽  
Density Dependent ◽  
Per Capita ◽  
Discrete Time Models ◽  
Complex Dynamical Behavior

The observation that no population can grow indefinitely and that most populations persist on ecological timescales implies that mechanisms of population regulation exist. Feedback mechanisms include competition for limited resources, cannibalism, and predation rates that vary with density. Density dependence occurs when per capita birth or death rates depend on population density. Density dependence is compensatory when the population growth rate decreases with population density and depensatory when it increases. The logistic model incorporates density dependence as a simple linear function. A population exhibiting logistic growth will reach a stable population size. Non-linear density-dependent terms can give rise to multiple equilibria. With discrete time models or time delays in density-dependent regulation, the approach to equilibrium may not be smooth—complex dynamical behavior is possible. Density-dependent feedback processes can compensate, up to a point, for natural and anthropogenic disturbances; beyond this point a population will collapse.

Adaptive Synchronization of Fractional-Order Coupled Neurons Under Electromagnetic Radiation

2020 ◽  
Vol 30 (03) ◽  
pp. 2050044
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Lyapunov Stability Theory ◽  
Neuronal Model ◽  
Adaptive Synchronization ◽  
Dynamical Characteristics ◽  
Single Controller ◽  
Improved Model ◽  
Complex Dynamical Behavior

In this paper, we investigate the dynamical characteristics of four-variable fractional-order Hindmarsh–Rose neuronal model under electromagnetic radiation. The numerical results show that the improved model exhibits more complex dynamical behavior with more bifurcation parameters. Meanwhile, based on the fractional-order Lyapunov stability theory, we propose two adaptive control methods with a single controller to realize chaotic synchronization between two coupled neurons. Finally, numerical simulations show the feasibility and effectiveness of the presented method.

Low-Velocity Impact on a Functionally Graded Circular Thin Plate

2006 ◽  
Author(s):  
Pantele Chelu ◽  
Liviu Librescu
Keyword(s):  
Plate Theory ◽  
Equation System ◽  
Functionally Graded ◽  
Low Velocity Impact ◽  
Thin Plates ◽  
Low Velocity ◽  
Alternative Analysis ◽  
Velocity Impact ◽  
Graded Material ◽  
The Impact

In this paper, an alternative analysis strategy based on a Wavelet-Galerkin scheme specially tailored to solve impact problems of functionally graded orthotropic thin plates subjected to low-velocity impact is presented. The plate considered to be circular, is assumed to be clamped on its lateral edge and has internal supports of rigid, elastic and viscoelastic types. The material properties of the plate are represented in the form of exponential functions of the thickness coordinate. A rigid spherical indenter impacts the plate. The study is based on the classical lamination plate theory (CLT). An advanced contact law of the Hertzian type is adopted. A nonlinear Volterra integral equation system is obtained in the following unknown functions: the impact force and the dynamic reaction forces at the rigid, elastic and viscoelastic internal point supports. Numerical simulations displaying the contact force, the transversal displacement and the penetration depth are graphically presented, and pertinent conclusions regarding the implications of incorporation of graded material systems are outlined.

scholarly journals Ice is born in low-mobility regions of supercooled liquid water

2019 ◽  
Vol 116 (6) ◽  
pp. 2009-2014 ◽  
Author(s):  
Martin Fitzner ◽  
Gabriele C. Sosso ◽  
Stephen J. Cox ◽  
Angelos Michaelides
Keyword(s):  
Liquid Water ◽  
Dynamical Behavior ◽  
Supercooled Liquid ◽  
Ice Nucleation ◽  
Water Molecules ◽  
Ice Crystal ◽  
Surrounding Water ◽  
Dynamical Heterogeneity ◽  
Complex Dynamical Behavior

When an ice crystal is born from liquid water, two key changes occur: (i) The molecules order and (ii) the mobility of the molecules drops as they adopt their lattice positions. Most research on ice nucleation (and crystallization in general) has focused on understanding the former with less attention paid to the latter. However, supercooled water exhibits fascinating and complex dynamical behavior, most notably dynamical heterogeneity (DH), a phenomenon where spatially separated domains of relatively mobile and immobile particles coexist. Strikingly, the microscopic connection between the DH of water and the nucleation of ice has yet to be unraveled directly at the molecular level. Here we tackle this issue via computer simulations which reveal that (i) ice nucleation occurs in low-mobility regions of the liquid, (ii) there is a dynamical incubation period in which the mobility of the molecules drops before any ice-like ordering, and (iii) ice-like clusters cause arrested dynamics in surrounding water molecules. With this we establish a clear connection between dynamics and nucleation. We anticipate that our findings will pave the way for the examination of the role of dynamical heterogeneities in heterogeneous and solution-based nucleation.

scholarly journals Chaos and complexity in a simple model of production dynamics

2000 ◽  
Vol 5 (3) ◽  
pp. 179-187 ◽  
Author(s):  
I. Katzorke ◽  
A. Pikovsky
Keyword(s):  
Simple Model ◽  
Dynamical Behavior ◽  
Production Costs ◽  
Order Flow ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
The Stability ◽  
The One ◽  
Production Dynamics ◽  
Complex Dynamical Behavior

We consider complex dynamical behavior in a simple model of production dynamics, based on the Wiendahl’s funnel approach. In the case of continuous order flow a model of three parallel funnels reduces to the one-dimensional Bernoulli-type map, and demonstrates strong chaotic properties. The optimization of production costs is possible with the OGY method of chaos control. The dynamics changes drastically in the case of discrete order flow. We discuss different dynamical behaviors, the complexity and the stability of this discrete system.

Structural Dynamical Modeling of Step Ladders

1995 ◽  
Vol 48 (11S) ◽  
pp. S102-S106
Author(s):  
Martin A. Eisenberg
Keyword(s):  
Dynamical Behavior ◽  
Experimental Results ◽  
Dynamic Loads ◽  
Dynamical Response ◽  
Dynamical Modeling ◽  
Dynamical Parameters ◽  
Complex Dynamical Behavior

Dynamic loads on step ladders are the result of interaction between climber and ladder. The complex dynamical behavior of the climber must be experimentally determined. An analysis of the dynamical response is presented to allow the extrapolation of experimental results to ladders of grossly different structural dynamical parameters from those on which the data are obtained. It is demonstrated that the climber characteristics dominate the dynamical response. Reliable quantitative measures of data applicability are obtained, not withstanding significant uncertainties regarding the details of the mechanics of motion.

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