Related papers: Dynamical Systems, Stability, and Chaos
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
The dynamics of two nonlinear Bloch systems is studied from the viewpoint of bifur- cation and a particular parameter space has been explored for the stability analysis based on stability criterion. This enables the choice of the desired…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
Mackey-Glass equation arises in the leukemia model. We generalize this equation to include fractional-order derivatives in two directions. The first generalization contains one whereas the second contains two fractional derivatives. Such…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
Methods and techniques of the theory of nonlinear dynamical systems and patterns can be useful in astrophysical applications. Some works on the subjects of dynamical astronomy, stellar pulsation and variability, as well as spatial…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
Hysteresis can be defined from a dynamical systems perspective with respect to equilibrium points. Consequently, hysteresis naturally lends itself as a topic to illustrate and extend concepts in a dynamical systems course. A number of…