Asymptotic Analysis of Bifurcations in Feedforward Networks

A feedforward network is a unidirectionally coupled chain of dynamical systems in which the first cell is coupled to itself, and each successive cell is coupled to the next one. Feedforward networks have gained considerable interest because of their potential to enhance signal amplification and to manipulate the frequency of oscillations. Indeed, it has been shown that the growth rate of the bifurcation undergone by the final cell is much larger than the expected square root growth rate associated with the standard Hopf bifurcation. In this paper, we present a new approach to studying this growth rate phenomenon. We employ a two-time-scale analysis and asymptotic approximations to detect behavior associated with the growth rate phenomenon that has not been previously observed. In particular, we show that the Hopf bifurcation is not the only bifurcation capable of exhibiting this large growth rate behavior. Using asymptotic methods we show that it is not a special property of the Hopf bifurcation that allows for this accelerated growth rate; it is a combination of the unidirectional coupling and the higher-degree nonlinearities that cause this effect. Furthermore, we show that this large growth rate need not persist away from the bifurcation. In fact, the growth rate is asymptotic to the standard square root growth rate as the bifurcation parameter increases.

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Response of Bromus valdivianus (Pasture Brome) Growth and Physiology to Defoliation Frequency Based on Leaf Stage Development

Agronomy ◽

10.3390/agronomy11102058 ◽

2021 ◽

Vol 11 (10) ◽

pp. 2058

Author(s):

Iván P. Ordóñez ◽

Ignacio F. López ◽

Peter D. Kemp ◽

Daniel J. Donaghy ◽

Yongmei Zhang ◽

...

Keyword(s):

Growth Rate ◽

Stomatal Conductance ◽

Root Growth ◽

Water Soluble ◽

Soluble Carbohydrates ◽

Leaf Stage ◽

Water Soluble Carbohydrates ◽

Stage Development ◽

Defoliation Frequency ◽

Root Growth Rate

The increase in drought events due to climate change have enhanced the relevance of species with greater tolerance or avoidance traits to water restriction periods, such as Bromus valdivianus Phil. (B. valdivianus). In southern Chile, B. valdivianus and Lolium perenne L. (L. perenne) coexist; however, the pasture defoliation criterion is based on the physiological growth and development of L. perenne. It is hypothesised that B. valdivianus needs a lower defoliation frequency than L. perenne to enhance its regrowth and energy reserves. Defoliation frequencies tested were based on B. valdivianus leaf stage 2 (LS-2), leaf stage 3 (LS-3), leaf stage 4 (LS-4) and leaf stage 5 (LS-5). The leaf stage development of Lolium perenne was monitored and contrasted with that of B. valdivianus. The study was conducted in a glasshouse and used a randomised complete block design. For Bromus valdivianus, the lamina length, photosynthetic rate, stomatal conductance, tiller number per plant, leaf area, leaf weights, root growth rate, water-soluble carbohydrates (WSCs) and starch were evaluated. Bromus valdivianus maintained six live leaves with three leaves growing simultaneously. When an individual tiller started developing its seventh leaf, senescence began for the second leaf (the first relevant leaf for photosynthesis). Plant herbage mass, the root growth rate and tiller growth were maximised at LS-4 onwards. The highest leaf elongation rate, evaluated through the slope of the lamina elongation curve of a fully expanded leaf, was verified at LS-4. The water-soluble carbohydrates (WSCs) increased at LS-5; however, no statistical differences were found in LS-4. The LS-3 and LS-2 treatments showed a detrimental effect on WSCs and regrowth. The leaf photosynthetic rate and stomatal conductance diminished while the leaf age increased. In conclusion, B. valdivianus is a ‘six-leaf’ species with leaf senescence beginning at LS-4.25. Defoliation at LS-4 and LS-5 was optimum for plant regrowth, maximising the aboveground plant parameters and total WSC accumulation. The LS-4 for B. valdivianus was equivalent to LS-3.5 for L. perenne. No differences related to tiller population in B. valdivianus were found in the different defoliation frequencies.

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Root Morphology of Eight Hybrid Oil Palms Under Iron (Fe) Toxicity

Ilmu Pertanian (Agricultural Science) ◽

10.22146/ipas.11254 ◽

2016 ◽

Vol 1 (1) ◽

pp. 013

Author(s):

Aprilia Ike Nurmalasari ◽

Eka Tarwaca Susila Putra ◽

Prapto Yudono

Keyword(s):

Growth Rate ◽

Root Growth ◽

Surface Area ◽

Root Morphology ◽

Block Design ◽

Dry Weight ◽

Root Volume ◽

Oil Palms ◽

Fe Toxicity ◽

Root Growth Rate

The research aims to study the change of morphology root characters of eight hybrid oil palms under iron toxicity (Fe). Field experiment done in arranged in a Randomized Complete Block Design (RCBD) two factors and three blocks as replications. The first factor was Fe concentration. It consists of two levels which are concentration 0µ.g-1 and concentration 600 µg.g-1 Fe. The second factor is the hybrid of oil palms which consists of eight hybrid oil palms as Yangambi, Avros, Langkat, PPKS 239, Simalungun, PPKS 718, PPKS 540 and Dumpy. Fe was applied by pouring FeSO4 solvent for 600 µg.g-1 500 ml.-1plant.-1day-1 on two months of plants after transplanting in the main nursery. Data were collected on root morphology and plant dry weight The data were analysis of variance (ANOVA) at 5% significanly, followed by Duncan's multiple range test (DMRT). The relationships by among variables were determined by correlation analysis. The results showed that Fe concentration 600 µg.g-1 inhibits relatively root growth rate, narrows surface area, reduces the diameter, and shrinks root volume of all hybrid oil palms tested. The slowing relatively root growth rate, narrowing of root surface area and root diameter also root volume shrinkage due to Fe stress. It was also shown that the dry weight of plants was inhibit by existing of Fe toxicity.

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Statistical analysis of root growth rate determinations

Environmental and Experimental Botany ◽

10.1016/0098-8472(80)90231-2 ◽

1980 ◽

Vol 20 (4) ◽

pp. 389-396 ◽

Cited By ~ 10

Author(s):

Christopher Cox ◽

Henry T. Davis ◽

Morton W. Miller ◽

Dominique Robertson

Keyword(s):

Growth Rate ◽

Statistical Analysis ◽

Root Growth ◽

Root Growth Rate

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Dependence of Root Growth Rate on Holoploid DNA Content

Russian Journal of Developmental Biology ◽

10.1134/s1062360419050114 ◽

2019 ◽

Vol 50 (5) ◽

pp. 257-260

Author(s):

N. V. Zhukovskaya ◽

E. I. Bystrova ◽

N. F. Lunkova ◽

V. B. Ivanov

Keyword(s):

Growth Rate ◽

Root Growth ◽

Dna Content ◽

Root Growth Rate

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Root Growth Rate of Soybean as Affected by Drought Stress 1

Agronomy Journal ◽

10.2134/agronj1987.00021962007900040004x ◽

1987 ◽

Vol 79 (4) ◽

pp. 607-614 ◽

Cited By ~ 69

Author(s):

Gerrit Hoogenboom ◽

M. G. Huck ◽

Curt M. Peterson

Keyword(s):

Growth Rate ◽

Drought Stress ◽

Root Growth ◽

Root Growth Rate

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Maturation of the tracheary elements in the roots of Pinus banksiana and Eucalyptus grandis

Canadian Journal of Botany ◽

10.1139/b01-057 ◽

2001 ◽

Vol 79 (7) ◽

pp. 844-849

Author(s):

J H Taylor ◽

C A Peterson

Keyword(s):

Growth Rate ◽

Root Growth ◽

Pinus Banksiana ◽

Eucalyptus Grandis ◽

Tracheary Element ◽

Reliable Indicator ◽

Root Tip ◽

Tracheary Elements ◽

Fluorescent Tracer ◽

Root Growth Rate

Tracheary elements of the xylem are responsible for the longitudinal (axial) transport of water and ions that have moved radially across the root. These vessel members and (or) tracheids mature some distance behind the root tip, and it is generally believed that this distance is directly related to root growth rate. To test this idea, the distances behind the root tip at which tracheary elements of pouch-grown Pinus banksiana Lamb. and Eucalyptus grandis W. Hill ex Maiden mature were examined. From each species, three root tip types (white, brown, and ectomycorrhizal short lateral) were assessed. Unlike previous studies of this topic, two methods of testing tracheary element maturity were employed concurrently. The first was anatomical and involved visualizing the deposition of lignin in the walls of the tracheids or vessel members. The second was functional and consisted of determining the capability of the tracheary elements to conduct a fluorescent, tracer dye. The distance behind the root tip at which the conductive xylem cells mature varied from 0.16 to 1.6 mm and was highly dependent on species and root type. No significant correlation was found between growth rate and proximity of tracheary element maturation to the tip for white roots. The presence of lignin in the tracheary element wall was not a reliable indicator of the cell's functional maturity.Key words: conductivity, development, roots, tracheary elements, xylem.

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CELLULAR MECHANISMS DETERMINING CHANGES IN ROOT GROWTH RATE IN VARIOUS EFFECTS

Book of proceedings of the All-Russian Scientific Conference with International Participation and Schools of Young Scientists "Mechanisms of resistance of plants and microorganisms to unfavorable environmental" (parts I, II) ◽

10.31255/978-5-94797-319-8-336-339 ◽

2018 ◽

Author(s):

N.V. Zhukovskaya ◽

E.I. Bystrova ◽

N.F. Lunkova ◽

V.B. Ivanov

Keyword(s):

Growth Rate ◽

Root Growth ◽

Cellular Mechanisms ◽

Root Growth Rate

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Clonal Variation in Lateral and Basal Rooting of Populus Irrigated with Landfill Leachate

Silvae Genetica ◽

10.1515/sg-2011-0005 ◽

2011 ◽

Vol 60 (1-6) ◽

pp. 35-44 ◽

Cited By ~ 3

Author(s):

R. S. Zalesny ◽

J. A. Zalesny

Keyword(s):

Growth Rate ◽

Root Growth ◽

Landfill Leachate ◽

Clonal Selection ◽

Lateral Roots ◽

Adventitious Rooting ◽

Clonal Variation ◽

Basal Roots ◽

Root Growth Rate ◽

Root Types

AbstractSuccessful establishment and productivity ofPopulusdepends upon adventitious rooting from: 1)lateral rootsthat develop from either preformed or induced primordia and 2)basal rootsthat differentiate from callus at the base of the cutting in response to wounding. Information is needed for phytotechnologies about the degree to whichPopulusadventitious rooting is controlled by effects of individual genotypes, waste waters used as alternative fertigation sources, and their interactions. Our objective was to irrigate twelvePopulusclones with well water (control) or municipal solid waste landfill leachate and to test for differences between initiation of lateral versus basal roots, as well as root growth rate and distributional trends for both root types. We evaluated number and length of lateral roots initiated from upper, middle, and lower thirds of the cutting, as well as basal callus roots. Overall, leachate irrigation affected lateral roots but not basal roots, and there was broad clonal variation between and within root types. On average, there were 129% more lateral than basal roots, which ranged from 3 to 27 (lateral) and 2 to 10 roots (basal). The percent advantage of number of roots from the middle portion of the cutting relative to other sections was 120% (upper), 193% (lower), and 24% (basal). Clones, treatments, and their interaction did not affect root growth rate, which ranged from 1.5 ± 0.6 to 3.4 ± 0.3 cm d−1, with a mean of 2.3 ± 0.2 cm d−1. These results contribute baseline information for clonal selection needed to establishPopulusfor phytotechnologies, energy, and fiber.

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