Publications about 'periodic inputs'
Articles in journal or book chapters
  1. M.A. Al-Radhawi, D. Angeli, and E.D. Sontag. On structural contraction of biological interaction networks. 2024. Note: To be submitted. Preprint in: arXiv contractions, contractive systems, matrix measures, logarithmic norms.
    In previous work, we have developed an approach to understanding the long-term dynamics of classes of chemical reaction networks, based on rate-dependent Lyapunov functions. In this paper, we show that stronger notions of convergence can be established by proving contraction with respect to non-standard norms. This enables us to show that such networks entrain to periodic inputs. We illustrate our theory with examples from signaling pathways and genetic circuits.

  2. E.V. Nikolaev, S.J. Rahi, and E.D. Sontag. Chaos in simple periodically-forced biological models. Biophysical Journal, 114:1232-1240, 2018. [PDF] Keyword(s): chaos, entrainment, systems biology, periodic inputs, subharmonic responses, biochemical systems, forced oscillations.
    What complicated dynamics can arise in the simplest biochemical systems, in response to a periodic input? This paper discusses two models that commonly appear as components of larger sensing and signal transduction pathways in systems biology: a simple two-species negative feedback loop, and a prototype nonlinear integral feedback. These systems have globally attracting steady states when unforced, yet, when subject to a periodic excitation, subharmonic responses and strange attractors can arise via period-doubling cascades. These behaviors are similar to those exhibited by classical forced nonlinear oscillators such as those described by van der Pol or Duffing equations. The lack of entrainment to external oscillations, in even the simplest biochemical networks, represents a level of additional complexity in molecular biology.

  3. S. J. Rahi, J. Larsch, K. Pecani, N. Mansouri, A. Y. Katsov, K. Tsaneva-Atanasova, E. D. Sontag, and F. R. Cross. Oscillatory stimuli differentiate adapting circuit topologies. Nature Methods, 14:1010-1016, 2017. [PDF] Keyword(s): biochemical networks, periodic behaviors, monotone systems, entrainment, oscillations, incoherent feedforward loop, feedforward, IFFL, systems biology.
    Elucidating the structure of biological intracellular networks from experimental data remains a major challenge. This paper studies two types of ``response signatures'' to identify specific circuit motifs, from the observed response to periodic inputs. In particular, the objective is to distinguish negative feedback loops (NFLs) from incoherent feedforward loops (IFFLs), which are two types of circuits capable of producing exact adaptation. The theory of monotone systems with inputs is used to show that ``period skipping'' (non-harmonic responses) is ruled out in IFFL's, and a notion called ``refractory period stabilization'' is also analyzed. The approach is then applied to identify a circuit dominating cell cycle timing in yeast, and to uncover a calcium-mediated NFL circuit in \emph{C.elegans} olfactory sensory neurons.

  4. G. Russo, M. di Bernardo, and E.D. Sontag. Global entrainment of transcriptional systems to periodic inputs. PLoS Computational Biology, 6:e1000739, 2010. [PDF] Keyword(s): contractive systems, contractions, systems biology, biochemical networks, gene and protein networks.
    This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to fixed limit cycles. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems.

Conference articles
  1. A. Duvall and E. D. Sontag. Global exponential stability or contraction of an unforced system do not imply entrainment to periodic inputs. In Proc. 2024 Automatic Control Conference, 2023. Note: To appear. Preprint in arXiv:2310.03241.
    It is often of interest to know which systems will approach a periodic trajectory when given a periodic input. Results are available for certain classes of systems, such as contracting systems, showing that they always entrain to periodic inputs. In contrast to this, we demonstrate that there exist systems which are globally exponentially stable yet do not entrain to a periodic input. This could be seen as surprising, as it is known that globally exponentially stable systems are in fact contracting with respect to some Riemannian metric. The paper also addresses the broader issue of entrainment when an input is added to a contractive system.

Internal reports
  1. E.D. Sontag. An observation regarding systems which converge to steady states for all constant inputs, yet become chaotic with periodic inputs. Technical report, arxiv 0906.2166, 2009. [PDF]



This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders.

Last modified: Thu Jun 27 23:19:31 2024
Author: sontag.

This document was translated from BibTEX by bibtex2html