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  • 1
    Electronic Resource
    Electronic Resource
    Bifurcation analysis of nephron pressure and flow regulation (1996)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 6 (1996), S. 280-287 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period-doubling cascades. Similar phenomena arise in response to increasing blood pressure. The numerical analyses are supported by existing experimental results on anesthetized rats. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166175
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  • 2
    Electronic Resource
    Electronic Resource
    Phase-locking regions in a forced model of slow insulin and glucose oscillations (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 5 (1995), S. 193-199 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We present a detailed numerical investigation of the phase-locking regions in a forced model of slow oscillations in human insulin secretion and blood glucose concentration. The bifurcation structures of period 2π and 4π tongues are mapped out and found to be qualitatively identical to those of several other periodically forced self-oscillating systems operating across a Hopf-bifurcation point. The numerical analyses are supplemented by clinical experiments. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166068
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  • 3
    Electronic Resource
    Electronic Resource
    Comments on the Theory of Unimodal Maps (1997)
    Springer
    Open systems & information dynamics 4 (1997), S. 379-392 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory, are called into attention.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009664631952
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  • 4
    Electronic Resource
    Electronic Resource
    Anomalous Statistics for Type-III Intermittency (1997)
    Springer
    Open systems & information dynamics 4 (1997), S. 393-405 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract The statistics for the distribution of laminar phases in type-IIIintermittency is examined for the map $$x_{n + 1} = - ((1 + \mu )x_n + x_n^3 )e^{ - bx_n^2 } $$ . Due to a strongly nonuniform reinjectionprocess, characteristic deviations from the normal statistics are observed.There is an enhancement of relatively long laminar phases followed by anabrupt cut-off of laminar phases beyond a certain length. The paper alsoexamines the bifurcation structure of two symmetrically coupled maps, eachdisplaying a subcritical period-doubling bifurcation. The conditions forsuch a pair of coupled maps to exhibit type-II intermittency are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009616700092
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  • 5
    Electronic Resource
    Electronic Resource
    Dynamics of a food web model of an aquatic ecosystem (1995)
    Springer
    Open systems & information dynamics 3 (1995), S. 237-254 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract The paper presents a model of an aquatic ecosystem with four species (bacteria, algae, zooplankton and fish) and with three different dead pools (detritus and accessible nutrients in the water column, and nutrients bound to the sediment). The structure of the model is that of a food web with the bacterial population representing the microbial loop. No distinction is made between different nutrients, and all uptake rates are expressed in terms of modified Monod kinetics. Though the model does not explicitly account for shifting abilities of the various species, the modified Monod kinetics enable predators with more than one prey (i.e., zooplankton and fish) to adjust their foraging habits in accordance with the conditions in the system. Simulations of the model show a variety of different solutions, ranging from simple oscillations with the annual periodicity of the external forcing to higher order chaos.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02228818
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  • 6
    Electronic Resource
    Electronic Resource
    Entrainment in a disaggregated economic long wave model (1995)
    Springer
    Open systems & information dynamics 3 (1995), S. 255-274 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract This paper investigates how mode-locking and other nonlinear dynamic phenomena arise through the interaction of two capital-producing sectors in a disaggregated economic long wave model. Each sector in isolation produces a self-sustained oscillation with a period and amplitude determined by the characteristics of that sector. However, the sectors interact through their mutual dependence on each other's output for their own production. When this coupling is accounted for, the two sectors tend to synchronize or lock together with a rational proportion between the periods. While keeping the aggregate equilibrium characteristics of the system constant, we study how this locking occurs as a function of the difference in capital lifetimes and as a function of the strength of the coupling between the sectors. Besides mode-locking and quasi-periodic behavior, the observed phenomena include cascades of period-doubling bifurcations, chaos, and intermittency. When the difference in capital lifetimes is very large, the coupled system tends to behave like a one-sector model with a reduced capital content of production.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02228819
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  • 7
    Electronic Resource
    Electronic Resource
    Mode-locking and chaos in a model of two coupled thermostatically controlled radiators (1995)
    Springer
    Open systems & information dynamics 3 (1995), S. 201-213 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract The paper examines a variety of nonlinear dynamic phenomena arising from the interaction between two thermostatically controlled radiators. Each system operates as a delayed, nonlinear control system and performs self-sustained opening and closing cycles when the slope of the regulator characteristics exceeds a critical value. The coupling is caused by heat exchange between the heated air volumes. As the sensitivity of one of the thermostats is changed, a devil's staircase of frequency-locked oscillations develops. For higher coupling strengths, mode-converting bifurcations, simultaneous periodic solutions and deterministic chaos can be observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02228816
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  • 8
    Electronic Resource
    Electronic Resource
    A model of enhancement and inhibition of HIV infection of monocytes by antibodies against HIV (1993)
    Springer
    Journal of biological physics 19 (1993), S. 133-145 
    Details
    ISSN: 1573-0689
    Keywords: Enhancement ; antibodies ; HIV ; mathematical model ; vaccine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract Antibodies (Ab) specific for epitopes on HIV glycoprotein gp120 or gp41 can inhibit or enhance HIV infection of human cellsin vitro. These effects may have significant implications both for the pathogenesis of chronic HIV infection and for vaccine development. A particularly puzzling findingin vitro is antibody dependent enhancement (ADE) at low concentrations of Ab while high concentrations of the same antibody inhibit infection. Similar phenomena have been observed for other enveloped viruses. Antibodies can inhibit infection by several mechanisms. However, by binding to receptors on target cells, virus bound antibodies can also enhance adhesion to these cells and thereby facilitate infection. We propose a mathematical model that describes how these two processes interact and hereby provide an explanation for the observed enhancement/neutralization phenomena. Simulation results were validated with good agreement against empirical data from antibody dependent enhancement of HIV infection of monocytoid (U937) cellsin vitro, and the model should be applicable to otherin vitro systems involving different cells and viruses. The model indicates that for the common type of HIV neutralizing antibody, acting at a post-CD4-binding step, there is a neutralizing ‘window’ defined by the affinity and concentration of antibody.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00700257
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  • 9
    Electronic Resource
    Electronic Resource
    Gene therapy of T helper cells in HIV infection: Mathematical model of the criteria for clinical effect (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 725-745 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper presents a mathematical analysis of the criteria for gene therapy of T helper cells to have a clinical effect on HIV infection. The analysis indicates that for such a therapy to be successful, it must protect the transduced cells against HIV-induced death. The transduced cells will not survive as a population if the gene therapy only blocks the spread of virus from transduced cells that become infected. The analysis also suggests that the degree of protection against disease-related cell death provided by the gene therapy is more important than the fraction of cells that is initially transduced. If only a small fraction of the cells can be transduced, transduction of T helper cells and transduction of haematopoietic progenitor cells will result in the same steady-state level of transduced T helper cells. For gene therapy to be efficient against HIV infection, our analysis suggests that a 100% protection against viral escape must be obtained. The study also suggests that a gene therapy against HIV infection should be designed to give the transduced cells a partial but not necessarily total protection against HIV-induced cell death, and to avoid the production of viral mutants insensitive to the gene therapy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458427
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  • 10
    Electronic Resource
    Electronic Resource
    Nonlinear mode-interaction in the macroeconomy (1992)
    Springer
    Annals of operations research 37 (1992), S. 185-215 
    Details
    ISSN: 1572-9338
    Keywords: Nonlinear economics ; mode-locking ; devil's staircase ; period doubling ; chaos ; fractal basin boundaries
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A central problem for a dynamic formulation of macroeconomic theory is how to explain the occurrence of different, relatively well-defined economic modes such as the short term business cycle, the construction (or Kuznets) cycle, and the economic long wave (or Kondratiev cycle). Equally important is a description of the various phenomena that can arise through interaction between these cycles. Modern nonlinear theory suggests that different cyclical modes may be entrained through the process of mode-locking, where the periods of the interacting modes adjust to one another, so as to attain a rational ratio. This type of interaction is well documented in physical and biological systems. However, despite the importance of the problem and abundant evidence for nonlinearity in the economy, modern concepts of nonlinear mode-interaction have not yet been applied to the problem of entrainment between economic cycles. We show how mode-locking and other highly nonlinear dynamic phenomena arise in a model of the economic long wave. The behavior of the model is mapped as a function of the frequency and amplitude of an external forcing, producing both a devil's staircase and a detailed Arnol'd tongue diagram. Two different routes to chaos are identified. The Lyapunov exponents are calculated, allowing the strength of the chaos to be assessed, and the fractal nature of the basins of attraction for two simultaneously existing periodic solutions is illustrated. The paper concludes with a discussion of the implications for economic theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02071056
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