scholarly journals GENERALIZED FRACTIONAL HYBRID HAMILTON–PONTRYAGIN EQUATIONS

2011 ◽  
Vol 08 (02) ◽  
pp. 245-264
Author(s):  
OANA CHIŞ ◽  
DUMITRU OPRIŞ
Keyword(s):  
Dynamical Systems ◽  
Credibility Theory ◽  
Langevin Equations ◽  
Hybrid Dynamical Systems ◽  
Probabilistic Theory ◽  
New Approach ◽  
Hamiltonian Equations ◽  
Liu Process ◽  
Fractional Wiener Process ◽  
Hybrid Equations

In this paper we present a new approach on the study of dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have investigated the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generalized fractional Liu process and the combination between them, generalized fractional hybrid process. Corresponding generalized fractional stochastic, respectively fuzzy, respectively hybrid dynamical systems were defined. We have applied the theory for generalized fractional hybrid Hamilton–Pontryagin (HP) equation and generalized fractional Hamiltonian equations. We have found fractional Langevin equations from the general fractional hybrid Hamiltonian equations. For these cases and specific parameters, numerical simulations were done.

scholarly journals The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109752
Author(s):  
Nathan J. Kong ◽  
J. Joe Payne ◽  
George Council ◽  
Aaron M. Johnson
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
Kalman Filtering ◽  
Hybrid Dynamical Systems

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

scholarly journals Identification of a Class of Hybrid Dynamical Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 875-882
Author(s):  
Stefano Massaroli ◽  
Federico Califano ◽  
Angela Faragasso ◽  
Mattia Risiglione ◽  
Atsushi Yamashita ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Hybrid Dynamical Systems

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

FREQUENCY SYNCHRONIZATION IN NETWORKS OF COUPLED OSCILLATORS, A MONOTONE DYNAMICAL SYSTEMS APPROACH

2009 ◽  
Vol 19 (12) ◽  
pp. 4107-4116 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Systems Approach ◽  
System Size ◽  
Coupling Scheme ◽  
Frequency Synchronization ◽  
Nonlinear Coupling ◽  
New Approach ◽  
Monotone Dynamical Systems

We propose a new approach to investigate the frequency synchronization in networks of coupled oscillators. By making use of the theory of monotone dynamical systems, we show that frequency synchronization occurs in networks of coupled oscillators, provided the coupling scheme is symmetric, connected, and strongly cooperative. Our criterion is independent of the system size, the coupling strength and the details of the connections, and applies also to nonlinear coupling schemes.

scholarly journals Theory of hybrid dynamical systems and its applications to biological and medical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4893-4914 ◽  
Author(s):  
Kazuyuki Aihara ◽  
Hideyuki Suzuki
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Systems Theory ◽  
Control Systems ◽  
Hybrid Systems ◽  
Hybrid Dynamical Systems ◽  
Medical Systems ◽  
Theme Issue ◽  
And Control

In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on–off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.

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