Appropriate time to apply control input to complex dynamical systems

Controlling a network structure has many potential applications many fields. In order to have an effective network control, not only finding good driver nodes is important, but also finding the optimal time to apply the external control signals to network nodes has a critical role. If applied in an appropriate time, one might be to control a network with a smaller control signals, and thus less energy. In this manuscript, we show that there is a relationship between the strength of the internal fluxes and the effectiveness of the external control signal. To be more effective, external control signals should be applied when the strength of the internal states is the smallest. We validate this claim on synthetic networks as well as a number of real networks. Our results may have important implications in systems medicine, in order to find the most appropriate time to inject drugs as a signal to control diseases.

[1]  S. Lowe,et al.  Control of apoptosis by p53 , 2003, Oncogene.

[2]  Xinghuo Yu,et al.  Optimizing Dynamical Network Structure for Pinning Control , 2016, Scientific Reports.

[3]  D-M Hu,et al.  Time-dependent sensitivity analysis of biological networks: coupled MAPK and PI3K signal transduction pathways. , 2006, The journal of physical chemistry. A.

[4]  Derek Ruths,et al.  Control Profiles of Complex Networks , 2014, Science.

[5]  Albert-László Barabási,et al.  Target control of complex networks , 2014, Nature Communications.

[6]  Young-Bum Kim,et al.  Corrigendum: Clusterin and LRP2 are critical components of the hypothalamic feeding regulatory pathway , 2013 .

[7]  F. Stokman,et al.  Evolution of sociology freshmen into a friendship network , 2003 .

[8]  Jon M. Kleinberg,et al.  The link-prediction problem for social networks , 2007, J. Assoc. Inf. Sci. Technol..

[9]  Stefan Wuchty,et al.  Controllability in protein interaction networks , 2014, Proceedings of the National Academy of Sciences.

[10]  Sharon L. Thompson-Schill,et al.  Brain and cognitive reserve: Translation via network control theory , 2016, Neuroscience & Biobehavioral Reviews.

[11]  Albert-László Barabási,et al.  Control Principles of Complex Networks , 2015, ArXiv.

[12]  D. Rowell.  2 . 14 Analysis and Design of Feedback Control Systems Time-Domain Solution of LTI State Equations , 2002 .

[13]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[14]  S. Mineka,et al.  Controllability and predictability in acquired motivation. , 1985, Annual review of psychology.

[15]  Matjaž Perc,et al.  Determining the flexibility of regular and chaotic attractors , 2006 .

[16]  Y. Oshika,et al.  P-glycoprotein-mediated acquired multidrug resistance of human lung cancer cells in vivo. , 1996, British Journal of Cancer.

[17]  Tatsuya Akutsu,et al.  Structural controllability of unidirectional bipartite networks , 2013, Scientific Reports.

[18]  Y. Tabuchi,et al.  Hyperthermia: an effective strategy to induce apoptosis in cancer cells , 2015, Apoptosis.

[19]  Wen-Xu Wang,et al.  Exact controllability of complex networks , 2013, Nature Communications.

[20]  Eric H Davidson,et al.  Gene regulation: gene control network in development. , 2007, Annual review of biophysics and biomolecular structure.

[21]  Z. Duan,et al.  Complex network synchronizability: analysis and control. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  M. Jalili,et al.  Target controllability with minimal mediators in complex biological networks. , 2020, Genomics.

[23]  Jinde Cao,et al.  Aperiodically intermittent stochastic stabilization via discrete time or delay feedback control , 2019, Science China Information Sciences.

[24]  Jie Ren,et al.  Controlling complex networks: How much energy is needed? , 2012, Physical review letters.

[25]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[26]  J. Vera,et al.  Computational Biology of Non-Coding RNA , 2019, Methods in Molecular Biology.

[27]  Gwe-Ya Kim,et al.  Application of systems and control theory-based hazard analysis to radiation oncology. , 2016, Medical physics.

[28]  C. Cotman,et al.  Apoptosis is induced by beta-amyloid in cultured central nervous system neurons. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Edward Ott,et al.  Controlling systems that drift through a tipping point. , 2014, Chaos.

[30]  Miguel A. F. Sanjuán,et al.  Partially controlling transient chaos in the Lorenz equations , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[31]  Zhenjun Ma,et al.  Energy efficient control of variable speed pumps in complex building central air-conditioning systems , 2009 .

[32]  Fang-Xiang Wu,et al.  Control principles for complex biological networks , 2018, Briefings Bioinform..

[33]  S. P. Cornelius,et al.  Realistic control of network dynamics , 2013, Nature Communications.

[34]  M. Perc,et al.  Control of dynamics via identical time-lagged stochastic inputs. , 2020, Chaos.

[35]  R. Marken,et al.  The Origins and Future of Control Theory in Psychology , 2015 .

[36]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[37]  M. Gearing,et al.  Correction: Corrigendum: Tonic inhibition in dentate gyrus impairs long-term potentiation and memory in an Alzheimer’s disease model , 2014, Nature Communications.

[38]  Xinghuo Yu,et al.  Controllability of complex networks: Choosing the best driver set , 2018, Physical Review E.

[39]  Matjaz Perc,et al.  Synchronization of Regular and Chaotic oscillations: the Role of Local Divergence and the Slow Passage Effect - a Case Study on calcium oscillations , 2004, Int. J. Bifurc. Chaos.

[40]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[41]  R. Kálmán.  Mathematical description of linear dynamical systems , 1963 .

[42]  Xinghuo Yu,et al.  Finding the Most Influential Nodes in Pinning Controllability of Complex Networks , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[43]  Lenka Zdeborová,et al.  The number of matchings in random graphs , 2006, ArXiv.