scholarly journals Nonlinear Dynamical Systems for Malaria Transmission and Control: Ross-Macdonald Model

2021 ◽  
pp. 1-10
Author(s):  
Chiwa Musa Dalah ◽  
◽  
Umar Yusuf Madaki ◽  
Keyword(s):  
Equilibrium State ◽  
Nonlinear Dynamical Systems ◽  
Control Program ◽  
Nonlinear Dynamical ◽  
Incubation Periods ◽  
The Stability ◽  
And Control ◽  
Disease Free ◽  
Insight Into ◽  
Leprosy Control

Malaria was declared an emergency in Nigeria and strategies for the control of Malaria in Nigeria were adopted to reduce its prevalence to a level at which the disease will no longer constitute public health problems. In this work, we presented a deterministic (Ross–Macdonald model susceptible, expose/ infected, infectious and recovered) model incorporating the method of control adopted by national Malaria and leprosy control program. We established the disease free and the endemic equilibrium states and carried out the stability analysis of the disease. Free and the equilibrium state. We also carried out numerical simulation of the model to have an insight into the dynamics of the model. We found out that the disease free equilibrium state is stable. The feedback dynamics from mosquito to human and back to mosquito involve considerable time due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a Ross–Macdonald model. The Jacobiant results showed that it would be very difficult to completely eradicate Malaria from Nigeria using the method adopted by national Malaria and leprosy control program.

WAVELET-BASED IDENTIFICATION AND CONTROL DESIGN FOR A CLASS OF NONLINEAR SYSTEMS

2006 ◽  
Vol 04 (01) ◽  
pp. 213-226 ◽  
Author(s):  
H. R. KARIMI ◽  
B. LOHMANN ◽  
B. MOSHIRI ◽  
P. JABEHDAR MARALANI
Keyword(s):  
Feedback Linearization ◽  
Nonlinear Dynamical Systems ◽  
Parameter Adaptation ◽  
Nonlinear Dynamical ◽  
Wavelet Networks ◽  
Modeling Errors ◽  
The Stability ◽  
And Control ◽  
Adaptive Control Law ◽  
Nonlinear Plant

In this paper, we extend the wavelet networks for identification and H∞ control of a class of nonlinear dynamical systems. The technique of feedback linearization, supervisory control and H∞ control are used to design an adaptive control law and also the parameter adaptation laws of the wavelet network are developed using a Lyapunov-based design. By some theorems, it will be proved that even in the presence of modeling errors, named network error, the stability of the overall closed-loop system and convergence of the network parameters and the boundedness of the state errors are guaranteed. The applicability of the proposed method is illustrated on a nonlinear plant by computer simulation.

Is There a Relation Between Synchronization Stability and Bifurcation Type?

2020 ◽  
Vol 30 (08) ◽  
pp. 2050123
Author(s):  
Zahra Faghani ◽  
Zhen Wang ◽  
Fatemeh Parastesh ◽  
Sajad Jafari ◽  
Matjaž Perc
Keyword(s):  
Complex Networks ◽  
Nonlinear Dynamical Systems ◽  
General Relation ◽  
Dynamical Behavior ◽  
Stability Function ◽  
Nonlinear Dynamical ◽  
Practical Applications ◽  
Stability Functions ◽  
Stability And Bifurcation ◽  
The Stability

Synchronization in complex networks is an evergreen subject with many practical applications across the natural and social sciences. The stability of synchronization is thereby crucial for determining whether the dynamical behavior is stable or not. The master stability function is commonly used to that effect. In this paper, we study whether there is a relation between the stability of synchronization and the proximity to certain bifurcation types. We consider four different nonlinear dynamical systems, and we determine their master stability functions in dependence on key bifurcation parameters. We also calculate the corresponding bifurcation diagrams. By means of systematic comparisons, we show that, although there are some variations in the master stability functions in dependence on bifurcation proximity and type, there is in fact no general relation between synchronization stability and bifurcation type. This has important implication for the restrained generalizability of findings concerning synchronization in complex networks for one type of node dynamics to others.

Adaptive Fuzzy Sliding Mode Control for a Class of Nonlinear Dynamical Systems

2011 ◽  
Vol 71-78 ◽  
pp. 4309-4312 ◽  
Author(s):  
Wen Da Zheng ◽  
Gang Liu ◽  
Jie Yang ◽  
Hong Qing Hou ◽  
Ming Hao Wang
Keyword(s):  
Sliding Mode Control ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Adaptive Sliding Mode Control ◽  
Nonlinear Dynamical ◽  
Mode Control ◽  
Fuzzy Sliding Mode ◽  
The Stability ◽  
Theory Of Lyapunov Stability

This paper presents a FBFN-based (Fuzzy Basis Function Networks) adaptive sliding mode control algorithm for nonlinear dynamic systems. Firstly, we designed an perfect control law according to the nominal plant. However, there always exists discrepancy between nominal and actual mode, and the FBFN was applied to approximate the uncertainty. After that, the adaptive law was designed to update the parameters of FBFN to alleviate the approximating errors. Based on the theory of Lyapunov stability, the stability of the adaptive controller was given with a sufficient condition. Simulation example was also given to illustrate the effectiveness of the method.

Bifurcation Control of Ro¨ssler System

2003 ◽  
Author(s):  
Z. Q. Wu ◽  
P. Yu
Keyword(s):  
Feedback Control ◽  
Nonlinear Dynamical Systems ◽  
Equilibrium Points ◽  
New Method ◽  
Control Law ◽  
Equilibrium Solutions ◽  
Nonlinear Dynamical ◽  
The Stability ◽  
Parameter Values ◽  
Feasible System

In this paper, a new method is proposed for controlling bifurcations of nonlinear dynamical systems. This approach employs the idea used in deriving the transition variety sets of bifurcations with constraints to find the stability region of equilibrium points in parameter space. With this method, one can design, via a feedback control, appropriate parameter values to delay either static, or dynamic or both bifurcations as one wishes. The approach is applied to consider controlling bifurcations of the Ro¨ssler system. The uncontrolled Ro¨ssler has two equilibrium solutions, one of which exhibits static bifurcation while the other has Hopf bifurcation. When a feedback control based on the new method is applied, one can delay the bifurcations and even change the type of bifurcations. An optimal control law is obtained to stabilize the Ro¨ssler system using all feasible system parameter values. Numerical simulations are used to verify the analytical results.

scholarly journals State Observation for Lipschitz Nonlinear Dynamical Systems Based on Lyapunov Functions and Functionals

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1424 ◽  
Author(s):  
Angelo Alessandri ◽  
Patrizia Bagnerini ◽  
Roberto Cianci
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Estimation Error ◽  
Stability Conditions ◽  
Nonlinear Dynamical ◽  
State Observation ◽  
State Observers ◽  
The Stability

State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are established in order to guarantee the asymptotic stability of the estimation error in a noise-free setting. Second, under the effect of system and measurement disturbances regarded as unknown inputs affecting the dynamics of the error, the proposed observers provide an estimation error that is input-to-state stable with respect to these disturbances. Lyapunov functions and functionals are adopted to prove such results. Third, simulations are shown to confirm the theoretical achievements and the effectiveness of the stability conditions we have established.

ON THE BIRTH OF MULTIPLE LIMIT CYCLES IN NONLINEAR SYSTEMS

1996 ◽  
Vol 06 (12b) ◽  
pp. 2587-2603 ◽  
Author(s):  
JORGE L. MOIOLA ◽  
GUANRONG CHEN
Keyword(s):  
Limit Cycles ◽  
Nonlinear Dynamical Systems ◽  
Approximation Technique ◽  
Hopf Bifurcations ◽  
Systems Methodology ◽  
Nonlinear Dynamical ◽  
Parameter Perturbations ◽  
Feedback Control Systems ◽  
Stability Indexes ◽  
The Stability

Degenerate (or singular) Hopf bifurcations of a certain type determine the appearance of multiple limit cycles under system parameter perturbations. In the study of these degenerate Hopf bifurcations, computational formulas for the stability indexes (i.e., curvature coefficients) are essential. However, such formulas are very difficult to derive, and so are usually computed by different approximation methods. Inspired by the feedback control systems methodology and the harmonic balance approximation technique, higher-order approximate formulas for such curvature coefficients are derived in this paper in the frequency domain setting. The results obtained are then applied to a study of nonlinear dynamical systems within the region of one periodic solution, bypassing a direct investigation of the multiple limit cycles and some tedious discussion of the complex multiplicity issue. Finally, we will show that several types of stability bifurcations can be controlled based on the results obtained in this paper.

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