Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.

"This book presents the result of a joint effort from different European Institutions within the framework of the EU funded project called SPARK II, devoted to device an insect brain computational model, useful to be embedded into autonomous robotic agents.
"Part I reports the biological background on Drosophila melanogaster with particular attention to the main centers which are used as building blocks for the implementation of the insect brain computational model.
Part II reports the mathematical approach to model the Central Pattern Generator used for the gait generation in a six-legged robot. Also the Reaction-diffusion principles in non-linear lattices are exploited to develop a compact internal representation of a dynamically changing environment for behavioral planning.
In Part III a software/hardware framework, developed to integrate the insect brain computational model in a simulated/real robotic platform, is illustrated. The different robots used for the experiments are also described. Moreover the problems related to the vision system were addressed proposing robust solutions for object identification and feature extraction.
Part IV includes the relevant scenarios used in the experiments to test the capabilities of the insect brain-inspired architecture taking as comparison the biological case. Experimental results are finally reported, whose multimedia can be found in the SPARK II web page: "www.spark2.diees.unict.it
"

This volume is a special Issue on "Dynamical Systems, Wave based computation and neuro inspired robots'^ based on a Course carried out at the CISM in Udine (Italy), the last week of September, 2003. From the topics treated within that Course, several new ideas were f- mulated, which led to a new kind of approach to locomotion and p- ception, grounded both on biologically inspired issues and on nonlinear dynamics. The Course was characterised by a high degree of multi disciplinarity. In fact, in order to conceive, design and build neuro inspired machines, it is necessary to deeply scan into different d- ciplines, including neuroscience. Artificial Intelligence, Biorobotics, Dynamical Systems theory and Electronics. New types of moving machines should be more closely related to the biological rules, not discarding the real implementation issues. The recipe has to include neurobiological paradigms as well as behavioral aspects from the one hand, new circuit paradigms, able of real time control of multi joint robots on the other hand. These new circuit paradigms are based on the theory of complex nonlinear dynamical systems, where aggregates of simple non linear units into ensembles of lattices, have the pr- erty that the solution set is much richer than that one shown by the single units. As a consequence, new solutions ^'emerge'\ which are often characterized by order and harmony.

The basic principles guiding sensing, perception and action in bio systems seem to rely on highly organised spatial-temporal dynamics. In fact, all biological senses, (visual, hearing, tactile, etc.) process signals coming from different parts distributed in space and also show a complex time evolution. As an example, mammalian retina performs a parallel representation of the visual world embodied into layers, each of which r- resents a particular detail of the scene. These results clearly state that visual perception starts at the level of the retina, and is not related uniquely to the higher brain centres. Although vision remains the most useful sense guiding usual actions, the other senses, ?rst of all hearing but also touch, become essential particularly in cluttered conditions, where visual percepts are somehow obscured by environment conditions. Ef?cient use of hearing can be learnt from acoustic perception in animals/insects, like crickets, that use this ancient sense more than all the others, to perform a vital function, like mating.

Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.

This book presents the result of a joint effort from different European Institutions within the framework of the EU funded project called SPARK II, devoted to device an insect brain computational model, useful to be embedded into autonomous robotic agents. Part I reports the biological background on Drosophila melanogaster with particular attention to the main centers which are used as building blocks for the implementation of the insect brain computational model. Part II reports the mathematical approach to model the Central Pattern Generator used for the gait generation in a six-legged robot. Also the Reaction-diffusion principles in non-linear lattices are exploited to develop a compact internal representation of a dynamically changing environment for behavioral planning. In Part III a software/hardware framework, developed to integrate the insect brain computational model in a simulated/real robotic platform, is illustrated. The different robots used for the experiments are also described. Moreover the problems related to the vision system were addressed proposing robust solutions for object identification and feature extraction. Part IV includes the relevant scenarios used in the experiments to test the capabilities of the insect brain-inspired architecture taking as comparison the biological case. Experimental results are finally reported, whose multimedia can be found in the SPARK II web page: www.spark2.diees.unict.it

The field of cellular neural networks (CNNs) is of growing importance in non linear circuits and systems and it is maturing to the point of becoming a new area of study in general nonlinear theory. CNNs emerged through two semi nal papers co-authored by Professor Leon O. Chua back in 1988. Since then, the attention that CNNs have attracted in the scientific community has been vast. For instance, there are international workshops dedicated to CNNs and their applications, special issues published in both the International Journal of Circuit Theory and in the IEEE Transactions on Circuits and Systems, and there are also Associate Editors appointed in the latter journal especially for the CNN field. All of this bears witness the importance that CNNs are gaining within the scientific community. Without doubt this book is a primer in the field. Its extensive coverage provides the reader with a very comprehensive view of aspects involved in the theory and applications of cellular neural networks. The authors have done an excellent job merging basic CNN theory, synchronization, spatio temporal phenomena and hardware implementation into eight exquisitely written chapters. Each chapter is thoroughly illustrated with examples and case studies. The result is a book that is not only excellent as a professional reference but also very appealing as a textbook. My view is that students as well professional engineers will find this volume extremely useful."

The basic principles guiding sensing, perception and action in bio systems seem to rely on highly organised spatial-temporal dynamics. In fact, all biological senses, (visual, hearing, tactile, etc.) process signals coming from different parts distributed in space and also show a complex time evolution. As an example, mammalian retina performs a parallel representation of the visual world embodied into layers, each of which r- resents a particular detail of the scene. These results clearly state that visual perception starts at the level of the retina, and is not related uniquely to the higher brain centres. Although vision remains the most useful sense guiding usual actions, the other senses, ?rst of all hearing but also touch, become essential particularly in cluttered conditions, where visual percepts are somehow obscured by environment conditions. Ef?cient use of hearing can be learnt from acoustic perception in animals/insects, like crickets, that use this ancient sense more than all the others, to perform a vital function, like mating.

This volume is a special Issue on "Dynamical Systems, Wave based computation and neuro inspired robots' DEGREES based on a Course carried out at the CISM in Udine (Italy), the last week of September, 2003. From the topics treated within that Course, several new ideas were f- mulated, which led to a new kind of approach to locomotion and p- ception, grounded both on biologically inspired issues and on nonlinear dynamics. The Course was characterised by a high degree of multi disciplinarity. In fact, in order to conceive, design and build neuro inspired machines, it is necessary to deeply scan into different d- ciplines, including neuroscience. Artificial Intelligence, Biorobotics, Dynamical Systems theory and Electronics. New types of moving machines should be more closely related to the biological rules, not discarding the real implementation issues. The recipe has to include neurobiological paradigms as well as behavioral aspects from the one hand, new circuit paradigms, able of real time control of multi joint robots on the other hand. These new circuit paradigms are based on the theory of complex nonlinear dynamical systems, where aggregates of simple non linear units into ensembles of lattices, have the pr- erty that the solution set is much richer than that one shown by the single units. As a consequence, new solutions DEGREES'emerge'\ which are often characterized by order and harmony.

In this monograph, new structures of neural networks in multidimensional domains are introduced. These architectures are a generalization of the Multi-layer Perceptron (MLP) in Complex, Vectorial and Hypercomplex algebra. The approximation capabilities of these networks and their learning algorithms are discussed in a multidimensional context. The work includes the theoretical basis to address the properties of such structures and the advantages introduced in system modelling, function approximation and control. Some applications, referring to attractive themes in system engineering and a MATLAB software tool, are also reported. The appropriate background for this text is a knowledge of neural networks fundamentals. The manuscript is intended as a research report, but a great effort has been performed to make the subject comprehensible to graduate students in computer engineering, control engineering, computer sciences and related disciplines.