scholarly journals Panic Spreading Model with Different Emotions under Emergency

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3190
Author(s):  
Rongjian Lv ◽  
Hua Li ◽  
Qiubai Sun
Keyword(s):  
Decision Making ◽  
Theoretical Model ◽  
Function Method ◽  
Cross Infection ◽  
Infected Person ◽  
Real Situation ◽  
Spreading Model ◽  
Lyapunov Function Method ◽  
The Stability ◽  
Harmful Effects

Emotion plays an important role in decision making. In an emergency, panic can spread among crowds through person-to-person communications and can cause harmful effects on society. The aim of this paper is to propose a new theoretical model in the context of epidemiology to describe the spread of panic under an emergency. First, according to divisions in personality in the context of psychology, groups are divided into a level-headed group and an impatient group. Second, individuals in the two groups have unique personalities. Thus, the level-headed group only infects within the group, while the impatient group considers emotional infection within the group and cross infection between the groups. Then, a nonlinear infection rate is used to describe the probability of infection after an infected person contacts a susceptible person, which is more in line with the real situation. After that, the level-headed group–impatient group nonlinear SIRS panic spreading model is developed. Stable analysis of the model is obtained using the Lyapunov function method to study the stability of the panic-free equilibrium and panic-permanence equilibrium. Finally, simulations are carried out to dynamically describe the spread process of group emotional contagion.

Neuro-Fuzzy Sliding Mode Control of Inverted Pendulum

2013 ◽  
Vol 711 ◽  
pp. 432-439
Author(s):  
Khedoudja Kherraz ◽  
Mustapha Hamerlain ◽  
Nouara Achour
Keyword(s):  
Function Method ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Robust Controller ◽  
Fuzzy Sliding Mode Control ◽  
Neuro Fuzzy ◽  
Lyapunov Function Method ◽  
Fuzzy Sliding Mode ◽  
Simulation Results ◽  
The Stability

In this paper we develop a robust controller based on sliding mode, neural network and fuzzy logic for the control of a class of under-actuated systems. The stability of the proposed controller is proved with the Lyapunov function method. Simulation results are made on an inverted pendulum.

The Stability of the Second-Order Model of the Damping Single Maching Infinite Bus Bar System

2013 ◽  
Vol 457-458 ◽  
pp. 1004-1007
Author(s):  
Hong Ying Luo ◽  
Jun Liu ◽  
Long Xing Li
Keyword(s):  
Lyapunov Function ◽  
Equilibrium Point ◽  
Single Machine ◽  
Function Method ◽  
Second Order ◽  
Order Model ◽  
Lyapunov Function Method ◽  
Single Machine Infinite Bus ◽  
The Stability ◽  
Second Order Model

This paper studies the stability of the second-order model of the damping single machine infinite bus bar system,by constructing a suitable Lyapunov function method,and discuss the stability of the equilibrium point,then obtains the attractive area.

scholarly journals Damped Perturbations of Systems with Center-Saddle Bifurcation

2021 ◽  
Vol 31 (09) ◽  
pp. 2150137
Author(s):  
Oskar A. Sultanov
Keyword(s):  
Autonomous System ◽  
Function Method ◽  
Critical Case ◽  
The Other ◽  
Unperturbed System ◽  
Driving Frequency ◽  
Bifurcation Parameter ◽  
Perturbed System ◽  
Lyapunov Function Method ◽  
The Stability

An autonomous system of ordinary differential equations on the plane with a center-saddle bifurcation is considered. The influence of a class of time damped perturbations is investigated. The particular solutions tending to the fixed points of the limiting system are considered. The stability of these solutions is analyzed by Lyapunov function method when the bifurcation parameter of the unperturbed system takes critical and noncritical values. Conditions that ensure the persistence of the bifurcation in the perturbed system are described. When the bifurcation is broken, a pair of solutions tending to a degenerate fixed point of the limiting system appears in the critical case. It is shown that, depending on the structure and the parameters of the perturbations, one of these solutions can be stable, metastable or unstable, while the other solution is always unstable. The proposed theory is applied to the study of autoresonance capturing in systems with quadratically varying driving frequency.

scholarly journals NEW COSMOLOGICAL SOLUTIONS AND STABILITY ANALYSIS IN FULL EXTENDED THERMODYNAMICS

1998 ◽  
Vol 07 (02) ◽  
pp. 177-187 ◽  
Author(s):  
LUIS P. CHIMENTO ◽  
ALEJANDRO S. JAKUBI ◽  
VICENÇ MÉNDEZ
Keyword(s):  
Function Method ◽  
De Sitter ◽  
Field Equations ◽  
Full Theory ◽  
New Exact Solutions ◽  
Lyapunov Function Method ◽  
Cosmological Solutions ◽  
Dissipative Fluid ◽  
The Stability ◽  
Nonlocal Transformation

The Einstein's field equations of FRW universes filled with a dissipative fluid described by full theory of causal transport equations are analyzed. New exact solutions are found using a nonlocal transformation on the nonlinear differential equation for the Hubble factor. The stability of the de Sitter and asymptotically Friedmannian solutions are analyzed using Lyapunov function method.

Stability analysis of nonlinear impulsive switched positive systems

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Yanzi Lin ◽  
Ping Zhao
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Function Method ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Positive Systems ◽  
Lyapunov Function Method ◽  
The Stability ◽  
Switched Positive Systems ◽  
Time Linear

Abstract In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

scholarly journals On the existence of periodic solution and the transition to chaos of Rayleigh-Duffing equation with application of gyro dynamic

2020 ◽  
Vol 5 (1) ◽  
pp. 93-108 ◽  
Author(s):  
Mohamed El-Borhamy ◽  
Nahla Mosalam
Keyword(s):  
Function Method ◽  
Fixed Point Theorems ◽  
Homoclinic Bifurcation ◽  
Qualitative Properties ◽  
Rayleigh Damping ◽  
Transition To Chaos ◽  
Lyapunov Function Method ◽  
The Stability ◽  
Theoretical Results ◽  
Euler’S Angles

AbstractIn this article, the study of qualitative properties of a special type of non-autonomous nonlinear second order ordinary differential equations containing Rayleigh damping and generalized Duffing functions is considered. General conditions for the stability and periodicity of solutions are deduced via fixed point theorems and the Lyapunov function method. A gyro dynamic application represented by the motion of axi-symmetric gyro mounted on a sinusoidal vibrating base is analyzed by the interpretation of its dynamical motion in terms of Euler’s angles via the deduced theoretical results. Moreover, the existence of homoclinic bifurcation and the transition to chaotic behaviour of the gyro motion in terms of main gyro parameters are proved. Numerical verifications of theoretical results are also considered.

scholarly journals Renovation Management Method in Neglected Buildings

2021 ◽  
Vol 13 (2) ◽  
pp. 929
Author(s):  
Beata Nowogońska ◽  
Magdalena Mielczarek
Keyword(s):  
Decision Making ◽  
Technical Condition ◽  
Irreversible Processes ◽  
Management Method ◽  
The Stability ◽  
Motivating Factor ◽  
Decision Making Support

Renovation works to buildings are often not carried out or there are shifts in time, which causes degradation of the building. The article presents an analysis of the consequences of abandoning renovation works. The aim of this article is to present a method of preliminarily planning renovations of a MRUB (Managing Renovation in Un-renovated Buildings). This method of decision-making support is based on the consequences in the case of the omission of renovations. The omission of renovations may lead to a threat to the stability of the building’s structure, threaten the lives of its users, and further damage the building by damaging further elements, or even cause a building disaster. Often, as a result of the abandonment of renovation, usually caused by the lack of the owner, improper manager, or irresponsible owners, these objects are degraded. The consequences of the failure of renovating buildings lead to irreversible processes of destruction. As a result of the research, it was found that it was not only a bad technical condition that was a prerequisite for carrying out the renovation. The consequences of the absence of renovation works, in addition to the technical condition, should be a motivating factor. The problem of the abandonment of renovations is presented using the example of the palace in Drwalewice.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

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