scholarly journals Stability Analysis of Swarm Heterogeneous Robots with Limited Field of View

2020 ◽  
Vol 19 (5) ◽  
pp. 942-966
Author(s):  
Takahiro Endo ◽  
Ryuma Maeda ◽  
Fumitoshi Matsuno
Keyword(s):  
Stability Analysis ◽  
Equilibrium State ◽  
Maximum Velocity ◽  
Field Of View ◽  
Robot Swarms ◽  
Swarm Robots ◽  
Heterogeneous Robots ◽  
Physical Limitations ◽  
The Stability ◽  
Navigation Method

This paper presents a stability analysis of swarm robots, a group of multiple robots. In particular, we focus on robot swarms with heterogeneous abilities, in which each robot has a different sensing range and physical limitations, including maximum velocity and acceleration. In addition, each robot has a unique sensing region with a limited angle field of view. We previously proposed a decentralized navigation method for such heterogeneous swarm robots consisting of one leader and multiple followers. With the decentralized navigation method, a single leader can navigate for followers while maintaining connectivity and satisfying the physical limitations unique to each robot; i.e., each follower has a target robot and follows it without violating its physical limitations. In this paper, we focus on a stability analysis of such swarm robots. When the leader moves at a constant velocity, we mathematically prove that the shape and orientations of all robots eventually converge to the equilibrium state. For this, we must first prove that the equilibrium state exists. Then, we show the convergence of the state to its equilibrium. Finally, we carry out experiments and numerical simulations to confirm the stability analysis, i.e., the convergence of the swarm robots to the equilibrium states.

scholarly journals Dynamics of a New Strain of the H1N1 Influenza A Virus Incorporating the Effects of Repetitive Contacts

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Puntani Pongsumpun ◽  
I-Ming Tang
Keyword(s):  
Stability Analysis ◽  
Equilibrium State ◽  
Influenza A Virus ◽  
Influenza A ◽  
Present Model ◽  
Numerical Solutions ◽  
H1n1 Influenza ◽  
Dynamical Modeling ◽  
Mathematical Equations ◽  
The Stability

The respiratory disease caused by the Influenza A Virus is occurring worldwide. The transmission for new strain of the H1N1 Influenza A virus is studied by formulating a SEIQR (susceptible, exposed, infected, quarantine, and recovered) model to describe its spread. In the present model, we have assumed that a fraction of the infected population will die from the disease. This changes the mathematical equations governing the transmission. The effect of repetitive contact is also included in the model. Analysis of the model by using standard dynamical modeling method is given. Conditions for the stability of equilibrium state are given. Numerical solutions are presented for different values of parameters. It is found that increasing the amount of repetitive contacts leads to a decrease in the peak numbers of exposed and infectious humans. A stability analysis shows that the solutions are robust.

Interface Stability Analysis of a Gel Material Surrounded by Air

2015 ◽  
Vol 1753 ◽  
Author(s):  
Carlos A. Garavito Garzon ◽  
M. Carme. Calderer ◽  
Satish Kumar
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Equilibrium State ◽  
Small Amplitude ◽  
Perturbation Methods ◽  
General Situation ◽  
Proposed Model ◽  
Harmonic Perturbation ◽  
The Stability ◽  
Over Time

ABSTRACTWe study the stability of small amplitude harmonic perturbation at the interface of a gel material surrounded by air. The equations describing the system's dynamics are solved using classical perturbation methods. Assuming that the amplitude decays over time, we establish conditions for the system to return to its equilibrium state. The proposed model includes the effect of the boundary conditions and can be extended to more general situation in which the material is surrounded by an arbitrary fluid.

scholarly journals Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 27 ◽  
Author(s):  
Gani Stamov ◽  
Stefania Tomasiello ◽  
Ivanka Stamova ◽  
Cvetelina Spirova
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Equilibrium State ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Delayed Neural Networks ◽  
The Stability ◽  
Impulsive Reaction

The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.

scholarly journals A Mathematical Model for the Eradication of Anopheles Mosquito and Elimination of Malaria

2020 ◽  
pp. 1-14
Author(s):  
Atanyi Yusuf Emmanuel ◽  
Abam Ayeni Omini
Keyword(s):  
Mathematical Model ◽  
Life Cycle ◽  
Steady State ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Anopheles Mosquito ◽  
Model Parameters ◽  
The Stability

A mathematical model to eliminate malaria by breaking the life cycle of anopheles mosquito using copepods at larva stage and tadpoles at pupa stage was derived aimed at eradicating anopheles pupa mosquito by introduction of natural enemies “copepods and tadpoles” (an organism that eats up mosquito at larva and pupa stage respectively). The model equations were derived using the model parameters and variables. The stability analysis of the free equilibrium states was analyzed using equilibrium points of Beltrami and Diekmann’s conditions for stability analysis of steady state. We observed that the model free equilibrium state is stable which implies that the equilibrium point or steady state is stable and the stability of the model means, there will not be anopheles adult mosquito in our society for malaria transmission. The ideas of Beltrami’s and Diekmann conditions revealed that the determinant and trace of the Jacobian matrix were greater than zero and less than zero respectively implying that the model disease free equilibrium state is stable. Hence, the number of larva that transforms to pupa is almost zero while the pupa that develop to adult is zero meaning the life-cycle is broken at the larva and pupa stages with the introduction of natural enemy. Maple was used for the symbolic and numerical solutions.

scholarly journals Stability Analysis of the Corruption Free Equilibrium of the Mathematical Model of Corruption in Nigeria

2020 ◽  
Vol 8 (2) ◽  
pp. 61-68
Author(s):  
Victor Akinsola ◽  
ADEYEMI BINUYO
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Operator Technique ◽  
Eigen Values ◽  
The Stability ◽  
The Mathematical Model

In this paper, a mathematical model of the transmission dynamics of corruption among populace is analyzed. The corruption free equilibrium state, characteristic equation and Eigen values of the corruption model were obtained. The basic reproductive number of the corruption model was also determined using the next generation operator technique at the corruption free equilibrium points. The condition for the stability of the corruption free equilibrium state was determined. The local stability analysis of the mathematical model of corruption was done and the results were presented and discussed accordingly. Recommendations were made from the results on measures to reduce the rate of corrupt practices among the populace.   

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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