scholarly journals Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems

2019 ◽  
Vol 24 (1) ◽  
pp. 13 ◽  
Author(s):  
Francisco Solis
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Dynamical Behavior ◽  
Discrete Dynamical Systems ◽  
Exponential Polynomial ◽  
Linear Dynamical System ◽  
The Stability ◽  
Polynomial Family ◽  
Complex Dynamical Behavior

In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, from which we show the intricate and complex dynamical behavior of their orbits.

scholarly journals STABILITY OF NON-LINEAR DYNAMICAL SYSTEM

2021 ◽  
Vol 9 (07) ◽  
pp. 275-283
Author(s):  
Anas Salim Youns ◽  
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Linear System ◽  
Three Dimension ◽  
Linear Dynamical System ◽  
Linear Dynamical Systems ◽  
Linearization Technique ◽  
The Public ◽  
Non Linear ◽  
The Stability

The mainobjective of this research is to study the stability of thenon-lineardynamical system by using the linearization technique of three dimension systems toobtain an approximate linear system and find its stability. We apply this technique to reaches to the stability of the public non linear dynamical systems of dimension. Finally, some proposed examples (example (1) and example (2)) are given to explain this technique and used the corollary.

Stability of Dynamical Systems With Multiple Nonlinearities

1987 ◽  
Vol 109 (4) ◽  
pp. 410-413 ◽  
Author(s):  
Norio Miyagi ◽  
Hayao Miyagi
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Lyapunov Function ◽  
Stability Region ◽  
Direct Method ◽  
Essential Feature ◽  
Point Of View ◽  
Stability Of Dynamical Systems ◽  
The Stability

This note applies the direct method of Lyapunov to stability analysis of a dynamical system with multiple nonlinearities. The essential feature of the Lyapunov function used in this note is a non-Lure´ type Lyapunov function which surpasses the Lure´-type Lyapunov function from the point of view of the stability region guaranteed. A modified version of the multivariable Popov criterion is used to construct non-Lure´ type Lyapunov function, which allow for the dynamical sytems with multiple nonlinearities.

scholarly journals Lifespan in a Primitive Boolean Linear Dynamical System

10.37236/5193 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Yaokun Wu ◽  
Yinfeng Zhu
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Minimum Size ◽  
Nonnegative Matrices ◽  
Linear Dynamical System ◽  
Linear Dynamical Systems

Let $\mathcal F$ be  a set of $k$ by $k$ nonnegative matrices such that every "long" product of elements of $\mathcal F$ is positive.   Cohen and Sellers (1982) proved that, then,  every such product of length $2^k-2$ over $\mathcal F$ must be positive. They suggested to investigate the minimum size of such $\mathcal F$ for which there exists a non-positive  product of length $2^k-3$ over $\mathcal F$ and they constructed one example of size $2^k-2$.  We construct one of size $k$ and further discuss relevant basic problems in the framework of Boolean linear dynamical systems. We also formulate several primitivity properties for general discrete dynamical systems.

A FAMILY OF COMPLETELY PERIODIC QUADRATIC DISCRETE DYNAMICAL SYSTEM

2008 ◽  
Vol 18 (05) ◽  
pp. 1425-1433 ◽  
Author(s):  
MILAN KUTNJAK ◽  
MATEJ MENCINGER
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Discrete Dynamical System ◽  
Dynamical Behavior ◽  
Basin Of Attraction ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Nonassociative Algebras ◽  
Rank 2 ◽  
The Basin Of Attraction

There is a one-to-one correspondence between homogeneous quadratic dynamical systems and commutative (possibly nonassociative) algebras. The corresponding theory for continuous systems is well known (c.f. [Markus, 1960; Walcher, 1991; Kinyon & Sagle, 1995]). In this paper the dynamics on the boundary of the basin of attraction of the origin, ∂ B Att (0), in homogeneous quadratic discrete dynamical systems is considered. In particular, we consider the dynamical behavior in a family of systems corresponding to a family of algebras [Formula: see text] which admits nilpotents of rank 2 and idempotents. The complete periodicity of a system (and the corresponding algebra) is defined and it is proven that for every n > 2 there are some systems/algebras from [Formula: see text] which are on ∂ BAtt(0) completely periodic with period n. The dynamics on ∂ B Att (0) is considered via a special class of polynomials Pn, n ∈ ℕ ∪ {0, -1}, recursively defined by Pn(α) = 2αPn-2(α) + Pn-1(α); P-1(α) = 0, P0(α) = 1, n ∈ ℕ.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

scholarly journals Chaotic Dynamical Systems Associated with Tilings of RN

2011 ◽  
pp. 19-41
Author(s):  
Lionel Rosier
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Homogeneous Space ◽  
Chaos Synchronization ◽  
Discrete Dynamical Systems ◽  
Dimensional Torus ◽  
Synchronization Mechanism ◽  
Chaotic Dynamical Systems ◽  
Regular Tiling

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of RN, whose most familiar example is provided by the N-dimensional torus TN. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup.

scholarly journals Discrete Dynamical Systems: A Brief Survey

2018 ◽  
Vol 14 (1) ◽  
pp. 35-51
Author(s):  
Sara Fernandes ◽  
Carlos Ramos ◽  
Gyan Bahadur Thapa ◽  
Luís Lopes ◽  
Clara Grácio
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Discrete Dynamical System ◽  
Discrete Dynamical Systems ◽  
Complex Numbers ◽  
Survey Paper ◽  
Number Systems ◽  
Mathematical Formalization ◽  
Research Students ◽  
Work Done

 Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization. Journal of the Institute of Engineering, 2018, 14(1): 35-51

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.

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