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Evolution of the Internet Topology and Traffic Dynamics of Data Packets
In recent years, the Internet has become one of the most influential media in our daily life, going beyond in its role as the basic infrastructure in...
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Orbit Dynamics, Stability and Chaos in Planetary Systems
Let us start with a problem of dynamical biology, which was posed about 800 years ago by Fibonacci1
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A Homotopy Continuation Solution of the Covariance Extension Equation
Algebraic geometry plays an important role in the theory of linear systems for (at least) three reasons. First, the Laplace transform turns...
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On Existence and Nonexistence of Limit Cycles for FitzHugh-Nagumo Class Models
In this paper we discuss the existence and non-existence of limit cycles of FitzHugh-Nagumo class models. The purpose is to clarify some unclear...
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From Empirical Data to Multi-Modal Control Procedures
In this paper we study the problem of generating control programs, i.e. strings of symbolic descriptions of control-interrupt pairs (or modes) from...
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The Kernel Memory Concept – A Paradigm Shift from Conventional Connectionism
In this chapter, the general concept of kernel memory (KM) is described, which is given as the basis for not only representing the general notion of...
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Modelling Abstract Notions Relevant to the Mind and the Associated Modules
This chapter is devoted to the remaining four modules within the AMS, i.e. 1) attention, 2) emotion, 3) intention, and 4) intuition module, and their...
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5. Nonlinear Systems with Autonomous Linear Parts
Denote $\displaystyle \Omega(r) = \{h \in C^n : \vert\vert h \vert\vert \leq...
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11. Input-to-State Stability
Let us consider a system described by the following equation in a Euclidean space C n :...
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Existence of Steady States. Positive and Nontrivial Steady States
Let us consider in C n the nonlinear equation...
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9. Lur’e Type Systems
In the present chapter we investigate the asymptotic stability of the system...
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Coupled Map Lattices: at the Age of Maturity
Coupled Map Lattices (CML) were simultaneously and independently introduced by K. Kaneko, R. Kapral and S. Kuznetsov in 1983–84 [1, 2, 3, 4, 5, 6]....
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Deterministic Control Theory
In this chapter we focus our attention on the open loop control of deterministic problems. We will see that the language of deterministic control...
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Optimization Problems
Several problems, for example Pontryagin’s maximum principle or the minimax problems of game theoretical approaches, require the determination of an...
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Synchronization in Complex Networks
The study of complex systems pervades all of science, from cell biology to ecology, from computer science to meteorology. A paradigm of a complex...
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Data Traffic, Topology and Congestion
We consider the interaction between the topology of a network and the tra.c carried along its channels. The binding elements between the topology and...
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Planet Formation
Motivating the study of planet formation is not difficult for any curious audience. One of the fundamental human questions is that of origins: “where...
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An Efficient QR Algorithm for a Hessenberg Submatrix of a Unitary Matrix
We describe an efficient procedure for implementing the Hessenberg QR algorithm on a class of matrices that we refer to as subunitary matrices. This...
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Arithmetic Properties of Observable Time Dependent Systems
Here we consider questions of discrete observability for linear systems of ordinary differential equations, extending work by Martin and Smith in...
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Endomorphisms of Hopf Algebras and a Little Bit of Control
Firstly this paper summarizes some of the the relations between control theory and coalgebra and Hopf algebra theory, particularly the fact that the...