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Sinusoidal Oscillator Circuits Reexamined

Prasad V. C.

International Journal of Electronics and Telecommunications

2018

Vol. 64, No. 1

77--81

Singular network condition is proposed to study oscillators. It states that a circuit is a potential oscillator if and only if the rank of the network matrix of size n X n is (n -1) at the frequency of oscillations. The dual (if it exists) and adjoint circuit of an oscillator are also oscillators. Limitations of Barkhausen’s approach are pointed out. It is explained that there are many ways to generate oscillations other than Barkhausen’s positive feedback configuration. The new approach emphasizes that appropriate D C inputs / initial conditions are important.

R. Thomas' Modeling of Biological Regulatory Networks : Introduction of Singular States in the Qualitative Dynamics

Richard A., Comet J-P., Bernot G.

Fundamenta Informaticae

2005

Vol. 65, nr 4

373--392

In the field of biological regulation, models extracted from experimental works are usually complex networks comprising intertwined feedback circuits. The overall behavior is difficult to grasp and the development of formal methods is needed in order to model and simulate biological regulatory networks. To model the behavior of such systems, R. Thomas and coworkers developed a qualitative approach in which the dynamics is described by a state transition system. Even if all steady states of the system can be detected in this formalism, some of them, the singular ones, are not formally included in the transition system. Consequently, temporal properties in which singular states have to be described, cannot be checked against the transition system. However, steady singular states play an essential role in the dynamics since they can induce homeostasis or multistationnarity and sometimes are associated to biological phenotypes. These observations motivated our interest for developing an extension of Thomas formalism in which all singular states are represented, allowing us to check temporal properties concerning singular states. We easily demonstrate in our formalism the previously demonstrated theorems giving the conditions for the steadiness of singular states. We also prove that our formalism is coherent with the Thomas one since all paths of the Thomas transition system are preserved in our one, which in addition includes singular states.