A new class of solvable dynamical systems

2008 ◽  
Vol 49 (5) ◽  
pp. 052701 ◽  
Author(s):  
Francesco Calogero
Keyword(s):  
Dynamical Systems ◽  
New Class ◽  
Solvable Dynamical Systems

scholarly journals Global Dynamical Systems Involving Generalized -Projection Operators and Set-Valued Perturbation in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yun-zhi Zou ◽  
Xi Li ◽  
Nan-jing Huang ◽  
Chang-yin Sun
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Banach Spaces ◽  
Equilibrium Points ◽  
Projection Operators ◽  
Initial Value ◽  
New Class ◽  
The Fixed Point Theorem ◽  
Generalized Projection Operators ◽  
Generalized Dynamical Systems

A new class of generalized dynamical systems involving generalizedf-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.

CHAOS, BIFURCATION AND ROBUSTNESS OF A CLASS OF HOPFIELD NEURAL NETWORKS

2011 ◽  
Vol 21 (03) ◽  
pp. 885-895 ◽  
Author(s):  
WEN-ZHI HUANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Chaotic Behavior ◽  
Robustness Analysis ◽  
Original System ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Computer Assisted ◽  
New Class

Chaos, bifurcation and robustness of a new class of Hopfield neural networks are investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated, the bifurcation plot and several important phase portraits are presented as well. By virtue of horseshoes theory in dynamical systems, rigorous computer-assisted verifications for chaotic behavior of the system with certain parameters are given, and here also presents a discussion on the robustness of the original system. Besides this, quantitative descriptions of the complexity of these systems are also given, and a robustness analysis of the system is presented too.

Bekenstein–Hawking entropy for discrete dynamical systems on sites

2019 ◽  
Vol 34 (32) ◽  
pp. 1950265
Author(s):  
Sh. Najmizadeh ◽  
M. Toomanian ◽  
M. R. Molaei ◽  
T. Nasirzade
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Upper Bound ◽  
Discrete Dynamical System ◽  
Discrete Dynamical Systems ◽  
New Class ◽  
A Site

In this paper, we extend the notion of Bekenstein–Hawking entropy for a cover of a site. We deduce a new class of discrete dynamical system on a site and we introduce the Bekenstein–Hawking entropy for each member of it. We present an upper bound for the Bekenstein–Hawking entropy of the iterations of a dynamical system. We define a conjugate relation on the set of dynamical systems on a site and we prove that the Bekenstein–Hawking entropy preserves under this relation. We also prove that the twistor correspondence preserves the Bekenstein–Hawking entropy.

The Stabilization Problem for Certain Class of Ecological Systems

1997 ◽  
Vol 07 (02) ◽  
pp. 247-251
Author(s):  
A. N. Kirillov
Keyword(s):  
Dynamical Systems ◽  
Ecological Systems ◽  
Constructive Method ◽  
Global Stabilization ◽  
Stabilization Problem ◽  
Piecewise Constant ◽  
New Class ◽  
Constant Control ◽  
Phase Coordinates ◽  
Piecewise Constant Control

The stabilization problem for dynamical systems is to find control providing stability of some sets in phase space. This problem is not solved in general for nonlinear systems. The ecological systems are nonlinear, as usual, with restrictions on phase coordinates and controls. In this paper we consider piecewise constant control stabilization. Some general results are obtained. A new class of population dynamical systems is introduced, for which the constructive method of global stabilization and controllability is given. The set of attraction is found.

Neutral networks: a combinatorial perspective

1999 ◽  
Vol 02 (03) ◽  
pp. 283-301 ◽  
Author(s):  
Stephan Kopp ◽  
Christian M. Reidys
Keyword(s):  
Combinatorial Optimization ◽  
Dynamical Systems ◽  
Computer Simulations ◽  
Evolutionary Change ◽  
Rna Molecules ◽  
New Class ◽  
Neutral Networks ◽  
Threshold Phenomenon ◽  
Theoretical Investigations ◽  
Sequential Dynamical Systems

The existence of neutral networks in genotype-phenotype maps has provided significant insight in theoretical investigations of evolutionary change and combinatorial optimization. In this paper we will consider neutral networks of two particular genotype-phenotype maps from a combinatorial perspective. The first map occurs in the context of folding RNA molecules into their secondary structures and the second map occurs in the study of sequential dynamical systems, a new class of dynamical systems designed for the analysis of computer simulations. We will prove basic properties of neutral nets and present an error threshold phenomenon for evolving populations of simulation schedules.

Singularities in the complex time plane and exactly solvable dynamical systems

1994 ◽  
Vol 72 (3-4) ◽  
pp. 147-151 ◽  
Author(s):  
W.-H. Steeb ◽  
Assia Fatykhova
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Numerical Study ◽  
Complex Time ◽  
Nonlinear Dynamical ◽  
Singularity Structure ◽  
Exactly Solvable ◽  
Solvable Dynamical Systems

A powerful tool in the study of nonlinear dynamical systems is the investigation of the singularity structure in the complex time plane. In most cases the singularity structure can only be found numerically. Here we give two models that can be solved exactly, i.e., we can give the singularities in the complex time plane. The two models play a central role in quantum mechanics. Then we compare them with the numerical study of the nonlinear differential equation.

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