摘要:

AbstractThis paper is the first part of a two part work that aims to introduce a new family of piecewise‐linear differential equations that exhibitchaoticbehaviour in numerical simulations and to provide a rigorous mathematical proof of its chaotic nature.The new family presented here has the same eigenvalue distribution as the well‐known Lorenz equations in its chaotic regime but has a different symmetry. It is a derivative of the recently investigated double‐scroll family of piecewise‐linear differential equations.1It differs, however, from the double‐scroll family in that its members have all real eigenvalues at the origin. In particular, since the associated eigenspaceEs(0) is similar to that of an overdamped linear circuit, we will henceforth refer to this family as theoverdamped double‐scroll family.We establish Chua's circuit2as a member of this family under appropriate conditions. Preliminary numerical simulations exhibit some interesting phenomena such as period‐doubling, periodic windows between chaotic behaviour, and strange attractors of differing geometric structure.Our approach in the rigorous analysis will be that employed for the double‐scroll family in Reference 1. We derive a linearly equivalent class of piecewise‐linear differential equations which includes the family simulated numerically as a special case. the necessary and sufficient condition for two piecewise‐linear vector fields belonging to this newoverdamped double‐scroll familyto be linearly equivalent is that their respective eigenvalues at respective equilibrium points be scalar multiples of each other. If the scalars are all identity, then we havelinear conjugacyof the vector fields. an explicitnormal formequation, in the sense of global bifurcation, is presented that is parametrized by its own eigenvalues.We find that linearly equivalent vector fields associated with the overdamped double‐scroll family exhibit the same global behaviour even though their equivalence is based on the local concept of normalized eigenvalues. In addition, the piecewise‐linear differential equations associated with these equivalent vector fields can be quite

ISSN:0098-9886    

DOI:10.1002/cta.4490160302

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1988

数据来源: WILEY

摘要:

AbstractThe computer‐aided testing (CAT) problem is inherently a large scale systems problem, it is essential to exploit whatever computational power is available to reduce the computational requirements for both on‐line and off‐line test processes. In particular, digital CAT algorithms often use some degree of parallel processing in their implementation. Therefore, the degree to which an analogue CAT algorithm can be implemented in parallel becomes a significant factor in determining its viability.In this paper, a parallel test algorithm and the associated architecture for the test system for analogue circuits and systems are proposed. the proposed test algorithm is applicable to testing multiple faults. Based on a combinatorial covering set approach, the conditions for the non‐sequential execution of the test algorithm is analysed and the parallel processing to generate the test results is also addressed.Although this paper is motivated on the discussions of analogue fault diagnosis, the proposed parallel algorithm and the combinatorial covering approach can also be applied to digital

ISSN:0098-9886    

DOI:10.1002/cta.4490160303

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1988

数据来源: WILEY

摘要:

AbstractA neural network approach is presented for transform image coding. It is shown that the three steps in the conventional transform image coding, i.e. the unitary transform of spatial domain image data, the quantization of the transform domain data and the binary coding of the quantized data, can be unified into a one‐step optimization problem. Then, the optimization problem is solved by an appropriately constructed Hopfield neural network whose input is the spatial domain image data and whose output is binary codes. A practical circuit implementation is given to perform the transform image coding. the circuit hasrM2neurons, whereris the bit‐rate, in bit/pixel, of the coding andM2is the size of the images. Each neuron consists of only a non‐linear voltage amplifier, a linear voltage‐controlled current source, a d.c. current source, a linear passive resistor, a linear passive capacitor, and a weighted voltage summer which can be made of a single op amp with some linear passive resistors. Moreover, each neuron islocallyconnected with no more thanb‐ 1 other neurons by wires, wherebis the maximum bit allocated to a transform domain coefficient. Therefore, our proposed approach is particularly suitable for low‐bit‐rate image coding and VLSI implementation. Furthermore, theanalogueandparallelnature of our approach matches perfectly the high‐speed requirement of real‐

ISSN:0098-9886    

DOI:10.1002/cta.4490160304

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1988

数据来源: WILEY

ISSN:0098-9886    

DOI:10.1002/cta.4490160305

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1988

数据来源: WILEY

ISSN:0098-9886    

DOI:10.1002/cta.4490160306

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1988

数据来源: WILEY

ISSN:0098-9886    

DOI:10.1002/cta.4490160307

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1988

数据来源: WILEY

ISSN:0098-9886    

DOI:10.1002/cta.4490160301

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1988

数据来源: WILEY