Modelling functional dynamical systems by piecewise linear systems with delay

Kahraman, Mustafa
Many dynamical systems in nature and technology involve delays in the interaction of variables forming the system. Furthermore, many of such systems involve external inputs or perturbations which might force the system to have arbitrary initial function. The conventional way to model these systems is using delay differential equations (DDE). However, DDEs with arbitrary initial functions has serious problems for finding analytical and computational solutions. This fact is a strong motivation for considering abstractions and approximations for dynamical systems involving delay. In this thesis, the piecewise linear systems with delay on piecewise constant part which is a useful subclass of hybrid dynamical systems is studied. We introduced various representations of these systems and studied the state transition conditions. We showed that there exists fixed point and periodic stable solutions. We modelled the genomic regulation of fission yeast cell cycle. We discussed various potential uses including approximating the DDEs and finally we concluded.


A unifying grid approach for solving potential flows applicable to structured and unstructured grid configurations
Cete, A. Ruhsen; Yuekselen, M. Adil; Kaynak, Uenver (Elsevier BV, 2008-01-01)
In this study, an efficient numerical method is proposed for unifying the structured and unstructured grid approaches for solving the potential flows. The new method, named as the "alternating cell directions implicit - ACDI", solves for the structured and unstructured grid configurations equally well. The new method in effect applies a line implicit method similar to the Line Gauss Seidel scheme for complex unstructured grids including mixed type quadrilateral and triangle cells. To this end, designated al...
Inference of switching networks by using a piecewise linear formulation
Akçay, Didem; Öktem, Hakan; Department of Scientific Computing (2005)
Inference of regulatory networks has received attention of researchers from many fields. The challenge offered by this problem is its being a typical modeling problem under insufficient information about the process. Hence, we need to derive the apriori unavailable information from the empirical observations. Modeling by inference consists of selecting or defining the most appropriate model structure and inferring the parameters. An appropriate model structure should have the following properties. The model...
Assessment of dynamic response FD algorithms by beam and plate FE computations
Alaylioglu, H.; Oral, Süha; Alaylıoğlu, Ayşe (Elsevier BV, 1988-10)
Improvement in understanding of the process of direct integration of the equations of motion through numerical dissipation parameter interaction is being regarded as one of the significant achievements of structural dynamics research over the past quarter century. The numerical software fraternity has extended one-step integration algorithms, emphasizing controllable approximation characteristics with respect to such factors as period elongation and amplitude decay. These studies have resulted in setting up...
Modeling a suspended nanotube oscillator
Toffoli, Hande; Arias, TA (American Chemical Society (ACS), 2005-03-01)
We present a general study of oscillations in suspended one-dimensional elastic systems clamped at each end, exploring a wide range of slack (excess length) and downward external forces. Our results apply directly to recent experiments in nanotube and silicon nanowire oscillators. We find the behavior to simplify in three well-defined regimes which we present in a dimensionless phase diagram. The frequencies of vibration of such systems are found to be extremely sensitive to slack.
Computational Design Emergence by Complexity and Morphogenesis
Gürsel Dino, İpek (null; 2016-12-17)
Emergence is the form or behavior of natural or artificial systems, which materializes due to the system components’ interactions with each other and their environment. Emergent properties are a result of processes of self-organization of complex systems such as swarming behavior of birds, insect colonies, immune systems, cities, the World Wide Web, social interactions, etc., as well as processes of natural morphogenesis that exhibit behavior of growth and adaptation. Emergent systems are also closely relat...
Citation Formats
M. Kahraman, “Modelling functional dynamical systems by piecewise linear systems with delay,” M.S. - Master of Science, Middle East Technical University, 2007.