Investigation of stabilization of a mathematical model of a dynamical system with random influence in the resonance case

1997 ◽  
Vol 49 (9) ◽  
pp. 1324-1329 ◽  
Author(s):  
I. A. Dzhalladova
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Resonance Case

Fuzzy Approximation by a Novel Levenberg–Marquardt Method for Two-Degree-of-Freedom Hypersonic Flutter Model

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Y. H. Wang ◽  
L. Zhu ◽  
Q. X. Wu ◽  
C. S. Jiang
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Approximation Scheme ◽  
Degree Of Freedom ◽  
Human Knowledge ◽  
Marquardt Method ◽  
Fuzzy Approximation ◽  
Levenberg Marquardt ◽  
Modification Factor ◽  
Two Degree Of Freedom

The two-degree-of-freedom (2DOF) hypersonic flutter dynamical system has strong aeroelastic nonlinearities, and it is very difficult to obtain a more precise mathematical model. By considering varying learning rate and σ-modification factor, a novel Levenberg– Marquardt (L–M) method is proposed, based on which, an online fuzzy approximation scheme for 2DOF hypersonic flutter model is established without any human knowledge. Compared with the standard L–M method, the proposed method can obtain faster converge speed and avoid parameter drift. Numerical simulations approve the advantages of the proposed scheme.

scholarly journals The synchronization of coupled stochastic systems driven by symmetric α-stable process and Brownian motion

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2219-2245
Author(s):  
Shahad Al-Azzawi ◽  
Jicheng Liu ◽  
Xianming Liu
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Brownian Motion ◽  
Gaussian Noise ◽  
Stochastic Systems ◽  
Stable Process ◽  
Symmetric Stable Process ◽  
And Brownian Motion ◽  
Coupled Dynamical System ◽  
Non Gaussian

The synchronization of stochastic differential equations (SDEs) driven by symmetric ?-stable process and Brownian Motion is investigated in pathwise sense. This coupled dynamical system is a new mathematical model, where one of the systems is driven by Gaussian noise, another one is driven by non- Gaussian noise. In this paper, we prove that the synchronization still persists for this coupled dynamical system. Examples and simulations are given.

scholarly journals New Chaotic Oscillator Derived from Class C Single Transistor-Based Amplifier

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jiri Petrzela
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
High Frequency ◽  
Piecewise Linear ◽  
Chaotic Oscillator ◽  
Chaotic Dynamical System ◽  
Transient Behaviour ◽  
Local Polynomial ◽  
Good Accordance ◽  
Class C

This paper describes a new autonomous deterministic chaotic dynamical system having a single unstable saddle-spiral fixed point. A mathematical model originates in the fundamental structure of the class C amplifier. Evolution of robust strange attractors is conditioned by a bilateral nature of bipolar transistor with local polynomial or piecewise linear feedforward transconductance and high frequency of operation. Numerical analysis is supported by experimental verification and both results prove that chaos is neither a numerical artifact nor a long transient behaviour. Also, good accordance between theory and measurement has been observed.

scholarly journals STATIONARY SOLUTIONS TO FOREST KINEMATIC MODEL

2009 ◽  
Vol 51 (1) ◽  
pp. 1-17 ◽  
Author(s):  
LE HUY CHUAN ◽  
TOHRU TSUJIKAWA ◽  
ATSUSHI YAGI
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Infinite Number ◽  
Kinematic Model ◽  
Stationary Solutions ◽  
Cross Diffusion ◽  
Stability And Instability ◽  
Math Biol ◽  
Forest Boundary ◽  
Boundary Dynamics

AbstractWe continue the study of a mathematical model for a forest ecosystem which has been presented by Y. A. Kuznetsov, M. Y. Antonovsky, V. N. Biktashev and A. Aponina (A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232). In the preceding two papers (L. H. Chuan and A. Yagi, Dynamical systemfor forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393–409; L. H. Chuan, T. Tsujikawa and A. Yagi, Aysmptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449), the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions.

Generalized mathematical model of the multiple-mass dynamical system of a vibration machine

1991 ◽  
Vol 27 (12) ◽  
pp. 1219-1225 ◽  
Author(s):  
I. I. Gerega ◽  
I. S. Lozovoi ◽  
M. R. Kozul'kevich ◽  
V. M. Shopa
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Vibration Machine

Autopoiesis and Cognition

2004 ◽  
Vol 10 (3) ◽  
pp. 327-345 ◽  
Author(s):  
Paul Bourgine ◽  
John Stewart
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Boundary Conditions ◽  
Living System ◽  
Random Dynamical System ◽  
Sensory Inputs ◽  
Autopoietic System ◽  
Definition Of

This article revisits the concept of autopoiesis and examines its relation to cognition and life. We present a mathematical model of a 3D tesselation automaton, considered as a minimal example of autopoiesis. This leads us to a thesis T1: “An autopoietic system can be described as a random dynamical system, which is defined only within its organized autopoietic domain.” We propose a modified definition of autopoiesis: “An autopoietic system is a network of processes that produces the components that reproduce the network, and that also regulates the boundary conditions necessary for its ongoing existence as a network.” We also propose a definition of cognition: “A system is cognitive if and only if sensory inputs serve to trigger actions in a specific way, so as to satisfy a viability constraint.” It follows from these definitions that the concepts of autopoiesis and cognition, although deeply related in their connection with the regulation of the boundary conditions of the system, are not immediately identical: a system can be autopoietic without being cognitive, and cognitive without being autopoietic. Finally, we propose a thesis T2: “A system that is both autopoietic and cognitive is a living system.”

scholarly journals Analysis of a Model for Coronavirus Spread

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 820 ◽  
Author(s):  
Youcef Belgaid ◽  
Mohamed Helal ◽  
Ezio Venturino
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Global Stability ◽  
Basic Reproduction Number ◽  
Local Stability ◽  
Reproduction Number ◽  
Early Stage ◽  
Asymptomatic Individuals ◽  
Restrictive Measures ◽  
Disease Free

The spread of epidemics has always threatened humanity. In the present circumstance of the Coronavirus pandemic, a mathematical model is considered. It is formulated via a compartmental dynamical system. Its equilibria are investigated for local stability. Global stability is established for the disease-free point. The allowed steady states are an unlikely symptomatic-infected-free point, which must still be considered endemic due to the presence of asymptomatic individuals; and the disease-free and the full endemic equilibria. A transcritical bifurcation is shown to exist among them, preventing bistability. The disease basic reproduction number is calculated. Simulations show that contact restrictive measures are able to delay the epidemic’s outbreak, if taken at a very early stage. However, if lifted too early, they could become ineffective. In particular, an intermittent lock-down policy could be implemented, with the advantage of spreading the epidemics over a longer timespan, thereby reducing the sudden burden on hospitals.

A mathematical model for neuronal differentiation in terms of an evolved dynamical system

2020 ◽  
Vol 156 ◽  
pp. 206-216 ◽  
Author(s):  
Hiroshi Watanabe ◽  
Takao Ito ◽  
Ichiro Tsuda
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Neuronal Differentiation

Adaptive Switch Control of Synchronizer for Dual Clutch Transmission

2015 ◽  
Vol 742 ◽  
pp. 500-504
Author(s):  
Hong Kui Li ◽  
Tong Li Lu ◽  
Jian Wu Zhang
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Control Strategy ◽  
Control Method ◽  
Hybrid Dynamical System ◽  
Dual Clutch Transmission ◽  
Synchronization Process ◽  
Switch Control ◽  
Simulation Results ◽  
Adaptive Switch

This paper focuses on developing a novel control strategy of synchronizer for dual clutch transmission. The synchronization process is investigated and a mathematical model of synchronizer is proposed. The paper proposes a switch control method for synchronizer which is a hybrid dynamical system. The simulation results demonstrate that the performance of the switch controller is reasonable and effective.

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