3,808 research outputs found

    Direct transition to high-dimensional chaos through a global bifurcation

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    In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step. The high-dimensional chaotic set is created in a heteroclinic global bifurcation that yields an infinite number of unstable tori.The mechanism is illustrated using a system constructed by coupling three Lorenz oscillators. So, the route presented here can be considered a prototype for high-dimensional chaotic behavior just as the Lorenz model is for low-dimensional chaos.Comment: 7 page

    Psi-series solutions of the cubic H\'{e}non-Heiles system and their convergence

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    The cubic H\'enon-Heiles system contains parameters, for most values of which, the system is not integrable. In such parameter regimes, the general solution is expressible in formal expansions about arbitrary movable branch points, the so-called psi-series expansions. In this paper, the convergence of known, as well as new, psi-series solutions on real time intervals is proved, thereby establishing that the formal solutions are actual solutions

    The Incredible Years Autism Spectrum and Language Delays Parent program: A pragmatic, feasibility randomized controlled trial

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    Behavior problems in children with autism spectrum disorders (ASD) are common and particularly stressful for parents. This study aimed to examine the feasibility of delivering a parenting program in existing services, and the feasibility of conducting a future large‐scale Randomized Controlled Trial evaluation of the effectiveness of the intervention. Parents of children aged 3–8 years with a diagnosis of ASD, or strongly suspected ASD were eligible to participate. A multicenter, pragmatic, feasibility randomized controlled trial was conducted in four specialist children's services in Wales. Families were randomly assigned to receive the Incredible YearsÂź Autism Spectrum and Language Delays (IY‐ASLD) parent program immediately or to a wait‐list, treatment as usual control condition. IY‐ASLD sessions were delivered once a week for 12 weeks. The primary outcomes related to feasibility (recruitment, retention, fidelity, and acceptability). Preliminary outcome analyses were conducted using covariance models controlling for study site and baseline scores. From October 5 to December 19, 2016, 58 families were randomized, 29 to IY‐ASLD and 29 to control. Three parents did not attend any sessions while 19 (73%) completed the program. Fidelity of delivery was high (88%), as was satisfaction with the program. Fifty‐three (91%) completed the follow‐up measures. All 95% CIs for effect sizes included zero in exploratory outcome analyses. This study supports the feasibility of delivering the IY‐ASLD in existing services with good levels of acceptability and fidelity evident. A larger randomized controlled trial is required to examine the effectiveness of the program. Autism Res 2019. © 2019 International Society for Autism Research, Wiley Periodicals, Inc
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