## 3 Citations

### Circuit Analysis using Monotone+Skew Splitting

- MathematicsArXiv
- 2022

—It is shown that the behavior of an m -port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a…

### Monotone one-port circuits

- Computer Science, MathematicsArXiv
- 2021

periodic input signals are shown to be mapped to periodic output signals, and these input-output behav-iors can be computed using a maximal monotone splitting algorithm, which decomposes the computation according to the circuit topology.

### Splitting algorithms and circuit analysis

- Computer ScienceArXiv
- 2022

This extended abstract presents new splitting algorithms specially suited to these structures, for interconnections of monotone and anti-monotone relations.

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It is shown that this characterization of oscillators as open systems that satisfy a particular dissipation inequality has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillations, and iii) for theglobal synchrony analysis in interConnections of identical oscillators.

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An extension of the absolute stability problem and of the Lagrange–Dirichlet theorem is presented, when the nonlinearities entering the model are considered within the class of monotone multivalued mappings.

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- PhysicsArXiv
- 2020

Maximal monotonicity is explored as a generalization of the linear theory of passivity, which allows for algorithmic system analysis of an important physical property of nonlinear 1-port circuits.

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It is concluded that such interconnections are well-posed in the sense of existence and uniqueness of solutions when the underlying linear system is passive and the static relation is maximal monotone.

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- Mathematics52nd IEEE Conference on Decision and Control
- 2013

This paper introduces the new class of incrementally port-Hamiltonian systems. This class can be obtained from standard port-Hamiltonian systems by replacing the composition of the Dirac structure…

### On critical points of the difference of two maximal monotone operators

- Mathematics
- 2015

Relying on the Yosida approximate, we present an algorithmic approach for finding a critical point of the difference of two maximal monotone operators in a finite dimensional real Hilbert space. The…

### Monotone networks

- MathematicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1960

Fundamental existence and uniqueness theorems for electrical networks of non-linear resistors are proved in an abstract form, as theorems of pure mathematics. The two groups from which the ‘currents’…

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- PhysicsBiological Cybernetics
- 2004

The dynamics of pattern formation is studied for lateral-inhibition type homogeneous neural fields with general connections and it is proved that there are five types of pattern dynamics.