The occurrence of riddled basins and blowout bifurcations in a parametric nonlinear system

In this paper, a two parameters family $F_{\beta_1,\beta_2}$ of maps of the plane living two different subspaces invariant is studied. We observe that, our model exhibits two chaotic attractors $A_i$, $i=0,1$, lying in these invariant subspaces and identify the parameters at which $A_i$ has a locally riddled basin of attraction or becomes a chaotic saddle. Then, the occurrence of riddled basin in the global sense is investigated in an open region of $\beta_1\beta_2$-plane. We semi-conjugate our system to a random walk model and define a fractal boundary which separates the basins of attraction of the two chaotic attractors, then we describe riddled basin in detail. We show that the model undergos a sequence of bifurcations: "a blowout bifurcation", "a bifurcation to normal repulsion" and "a bifurcation by creating a new chaotic attractor with an intermingled basin". Numerical simulations are presented graphically to confirm the validity of our results.Comment: 26 pages, 15 figure

Comparison between diuretic urography (IVP) and diuretic renography for diagnosis of ureteropelvic junction obstruction in children

Background: Ureteropelvic junction obstruction (UPJO) is one of the most common causes of urinary tract obstruction in children. Several methods are used to diagnose upper urinary tract obstruction including renal ultrasonography (US), intravenous pyelogram (IVP), diuretic renography (DR), magnetic resonance urography (MRU) and antegrade or retrograde pyelography. Nowadays it is suggested to use diuretic renography as the best method for diagnosing of UPJO. There is no comparative study between IVP and DR scan for diagnosis of UPJO in children. Objectives: The aim of the present study was to compare IVP with furosemide injection and diuretic renography in diagnosis of clinically significant UPJO. Patients and Methods: This was a cross sectional study performed in 153 UPJO suspected children (121 boys, 32 girls) based on US findings in cases presented with urinary tract infection (UTI), prenatal hydronephrosis, abdominal/flank pain, abdominal mass and hematuria. Renal ultrasound was used as an initial screening tool for detection of urinary tract abnormality. Vesicoureteral reflux (VUR) was ruled out by voiding cystourethrography (VCUG). Serum creatinin, blood urea nitrogen, urinalysis and urine culture was screened in all cases. IVP with furosemide and DR were performed as soon as possible after the mentioned workup. Results: During a five year period, 46 out of 153 patients were diagnosed as UPJO based on diuretic renography: the age ranged from 4 months to 13 years (mean: 3.1 ± 0.78 years). There was a significant higher (76) proportion of UPJO in the boys and in the left side (78). The sensitivity of IVP with furosemide injection in diagnosis of UPJO was 91.3 whereas DR was accepted as standard for diagnostic procedure in diagnosis of UPJO. Conclusions: Although DR is accepted as the best method for diagnosis of UPJO, we found a small sensitivity difference between IVP and DR in kidneys with normal or near normal function. In many settings such as small cities lacking facilities for advanced isotope imaging technology, use of IVP with diuretic maybe an acceptable procedure for diagnosis of UPJO. © 2016, Growth & Development Research Center