Loss Of Determinacy Research Articles

Loss of Determinacy at Small Scales, with Application to Multiple Timescale and Nonsmooth Dynamics

A singularity is described that creates a forward time loss of determinacy in a two-timescale system, in the limit where the timescale separation is large. We describe how the situation can arise in a dynamical system of two fast variables and three slow variables or parameters, with weakly coupling between the fast variables. A wide set of initial conditions enters the [Formula: see text]-neighborhood of the singularity, and explodes back out of it to fill a large region of phase space, all in finite time. The scenario has particular significance in the application to piecewise-smooth systems, where it arises in the blow up of dynamics at a discontinuity and is followed by abrupt recollapse of solutions to “hide” the loss of determinacy, and yet leave behind a remnant of it in the global dynamics. This constitutes a generalization of a “micro-slip” phenomenon found recently in spring-coupled blocks, whereby coupled oscillators undergo unpredictable stick-slip-stick sequences instigated by a higher codimension form of the singularity. The indeterminacy is localized to brief slips events, but remains evident in the indeterminate sequencing of near-simultaneous slips of multiple blocks.

Micro-Slip as a Loss of Determinacy in Dry-Friction Oscillators

Dry-friction contacts in mechanical oscillators can be modeled using nonsmooth differential equations, and recent advances in dynamical theory are providing new insights into the stability and uniqueness of such oscillators. A classic model is that of spring-coupled masses undergoing stick-slip motion on a rough surface. Here, we present a phenomenon in which multiple masses transition from stick to slip almost simultaneously, but suffer a brief loss of determinacy in the process. The system evolution becomes many-valued, but quickly collapses back down to an infinitesimal set of outcomes, a sort of “micro-indeterminacy”. Though fleeting, the loss of determinacy means masses may each undergo different microscopic sequences of slipping events, before all masses ultimately slip. The microscopic loss of determinacy is visible in local changes in friction forces, and in creating a bistability of global stick-slip oscillations. If friction forces are coupled between the oscillators then the effect is more severe, as solutions are compressed instead onto two (or more) macroscopically different outcomes.

Development of phytoplasma-induced flower symptoms in Arabidopsis Thaliana

A reliable model for the study of the molecular events leading to floral symptoms during plant–phytoplasma interaction was established by developing an efficient protocol for the infection of Arabidopsis thaliana with the Italian Clover Phyllody (ICPh) phytoplasma. ICPh phytoplasma infection of different A. thaliana ecotypes resulted in a wide range of symptom patterns. Ecotype Col-0 was selected for the repeatable time course and the severity of flower developmental alterations. By inoculating Col-0 at 30 days after germination with ICPh phytoplasma in short day, flowers were produced with increasingly severe symptoms, from carpels modification to virescence, phyllody, loss of determinacy and loss of organ developmental pattern. Gene expression analysis showed strong down regulation of some homeotic genes involved in flowering and genes involved in the gibberellin metabolism. Common morphological features were detected in phytoplasma-infected wild type plants and healthy mutants impaired in the gene functions that were found to be down-regulated in the infected plants. Evidence from the analysis of morphological alterations and from the results of quantitative real time PCR pointed to a central role of the deregulation of SEPALLATA genes, that are involved in flower development and hormonal control.

Sliding bifurcations and non-determinism in systems with switching

AbstractDynamical events associated with loss of determinacy in piecewise-smooth dynamical systems are reviewed. The causes of non-determinacy are discussed, and the conditions for their occurence in general systems are derived. These events can be characterized in terms of recently classified catastrophic sliding bifurcations and a non-deterministic form of chaos, which are shown to provide generic scenarios for non-determinacy to affect stable dynamical behaviour. The particular conditions for these are derived in a canonical (Lur'e) model of switched feedback control, and explicit examples are given in two and three dimensions.

The MADS box gene FBP2 is required for SEPALLATA function in petunia.

The ABC model, which was accepted for almost a decade as a paradigm for flower development in angiosperms, has been subjected recently to a significant modification with the introduction of the new class of E-function genes. This function is required for the proper action of the B- and C-class homeotic proteins and is provided in Arabidopsis by the SEPALLATA1/2/3 MADS box transcription factors. A triple mutant in these partially redundant genes displays homeotic conversion of petals, stamens, and carpels into sepaloid organs and loss of determinacy in the center of the flower. A similar phenotype was obtained by cosuppression of the MADS box gene FBP2 in petunia. Here, we provide evidence that this phenotype is caused by the downregulation of both FBP2 and the paralog FBP5. Functional complementation of the sepallata mutant by FBP2 and our finding that the FBP2 protein forms multimeric complexes with other floral homeotic MADS box proteins indicate that FBP2 represents the same E function as SEP3 in Arabidopsis.