scholarly journals Random local complex dynamics

2018 ◽  
Vol 40 (8) ◽  
pp. 2156-2182
Author(s):  
LORENZO GUERINI ◽  
HAN PETERS
Keyword(s):  
Fixed Point ◽  
Probability Measure ◽  
Complex Dynamics ◽  
Linear Part ◽  
Interesting Case ◽  
Holomorphic Maps ◽  
Deterministic Case ◽  
Local Complex ◽  
The Family ◽  
The Stability

The study of the dynamics of an holomorphic map near a fixed point is a central topic in complex dynamical systems. In this paper, we will consider the corresponding random setting: given a probability measure $\unicode[STIX]{x1D708}$ with compact support on the space of germs of holomorphic maps fixing the origin, we study the compositions $f_{n}\circ \cdots \circ f_{1}$, where each $f_{i}$ is chosen independently with probability $\unicode[STIX]{x1D708}$. As in the deterministic case, the stability of the family of the random iterates is mostly determined by the linear part of the germs in the support of the measure. A particularly interesting case occurs when all Lyapunov exponents vanish, in which case stability implies simultaneous linearizability of all germs in $\text{supp}(\unicode[STIX]{x1D708})$.

scholarly journals Complex dynamics of a discrete-time prey-predator system with Allee effect

2021 ◽  
Author(s):  
Özlem Gümüş
Keyword(s):  
Fixed Point ◽  
Discrete Time ◽  
Allee Effect ◽  
Control Method ◽  
Complex Dynamics ◽  
Hybrid Control ◽  
Chaotic Behavior ◽  
The Stability ◽  
Predator System ◽  
Positive Fixed Point

In this paper, we investigate the stability and bifurcation of a discrete-time prey-predator system which is subject to an Allee effect on prey population. It is concluded that the system undergoes flip and Neimark- Sacker bifurcations in a small neigborhood of the unique positive fixed point which depends on the number of prey-predator. The chaotic behavior that emerges with Neimark-Sacker bifurcation is controlled by the OGY method and hybrid control method. Moreover, the numerical simulations are done to demonsrate the theoratical results.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals On the stability of set-valued functional equations with the fixed point alternative

2012 ◽  
Vol 2012 (1) ◽  
pp. 81 ◽  
Author(s):  
Hassan Kenary ◽  
Hamid Rezaei ◽  
Yousof Gheisari ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
The Stability

Use of an Ambulatory Infusion Pump in a 12-Year-Old with Salmonella Osteomyelitis

DICP ◽  
1989 ◽  
Vol 23 (5) ◽  
pp. 379-381
Author(s):  
Allen J. Vaida ◽  
Chantel J. Mattiucci ◽  
Steven A. Shapiro ◽  
Linda A. Gusenko ◽  
Anna M. King
Keyword(s):  
Cost Saving ◽  
Antibiotic Therapy ◽  
Infusion Pump ◽  
Medication Administration ◽  
Sterile Water ◽  
Home Therapy ◽  
Parenteral Antibiotic ◽  
The Family ◽  
The Stability ◽  
Salmonella Osteomyelitis

A 12-year-old girl with sickle cell hemoglobinopathy presented with a Salmonella osteomyelitis of her right humerus requiring six weeks of parenteral antibiotic therapy. Home therapy was evaluated. Due to the frequency of the medication administration (every six hours) and the apprehension of the family members, a Pharmacia-Deltec CADD-VT Infusion Pump was chosen for drug administration. Based on the stability of ampicillin, 1.3 g q6h was administered to provide a minimum of 1 g for the last dose of a 24-hour cycle. Ampicillin 6 g contained in 100 mL of sterile water for injection provided a 60 mg/mL solution with an osmolarity of 347 mOsmol. The pump was programmed to deliver 22 mL of solution over one hour, every six hours. A keep-vein-open rate of 0.2 mL/h maintained line patency. A 100 mL cassette of solution prepared daily was replaced on the pump by a home therapy nurse each morning. At the end of six weeks of therapy, the osteomyelitis was eradicated. We found the use of an ambulatory infusion pump an effective, convenient, and cost-saving method of treatment for our patient.

scholarly journals Characterization of Cocycle Attractors for Nonautonomous Reaction–Diffusion Equations

2016 ◽  
Vol 26 (08) ◽  
pp. 1650135 ◽  
Author(s):  
C. A. Cardoso ◽  
J. A. Langa ◽  
R. Obaya
Keyword(s):  
Chaotic Dynamics ◽  
Linear Part ◽  
Reaction Diffusion ◽  
Positive Cone ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Minimal Set ◽  
Full Characterization ◽  
The Stability

In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction–diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li–Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee–Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.

Stability of slender inverted flags and rods in uniform steady flow

2016 ◽  
Vol 809 ◽  
pp. 873-894 ◽  
Author(s):  
John E. Sader ◽  
Cecilia Huertas-Cerdeira ◽  
Morteza Gharib
Keyword(s):  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Flow Direction ◽  
Flow Speed ◽  
Uniform Flow ◽  
Biological Phenomena ◽  
Cantilever Length ◽  
The Stability ◽  
Elastic Sheets ◽  
Clamped Edge

Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an ‘inverted flag’. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.

scholarly journals Chaos and Stability in a New Iterative Family for Solving Nonlinear Equations

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 101
Author(s):  
Alicia Cordero ◽  
Marlon Moscoso-Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Fixed Points ◽  
Periodic Orbits ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Complex Dynamics ◽  
Convergence Properties ◽  
Parameter Spaces ◽  
Numerical Tests ◽  
The Family ◽  
Dynamics Stability

In this paper, we present a new parametric family of three-step iterative for solving nonlinear equations. First, we design a fourth-order triparametric family that, by holding only one of its parameters, we get to accelerate its convergence and finally obtain a sixth-order uniparametric family. With this last family, we study its convergence, its complex dynamics (stability), and its numerical behavior. The parameter spaces and dynamical planes are presented showing the complexity of the family. From the parameter spaces, we have been able to determine different members of the family that have bad convergence properties, as attracting periodic orbits and attracting strange fixed points appear in their dynamical planes. Moreover, this same study has allowed us to detect family members with especially stable behavior and suitable for solving practical problems. Several numerical tests are performed to illustrate the efficiency and stability of the presented family.

Separating the Contributions in Localization Methods: A Technique to Enhance Identification of Damping Related Parameters

1999 ◽  
Author(s):  
Hervé Algrain ◽  
Calogero Conti ◽  
Pierre Dehombreux
Keyword(s):  
Finite Element ◽  
Model Updating ◽  
Element Model ◽  
Dynamic Responses ◽  
Finite Element Model Updating ◽  
Global Localization ◽  
Localization Method ◽  
The Family ◽  
Family Based ◽  
The Stability

Abstract Finite Element Model Updating has for objective to increase the correlation between the experimental dynamic responses of a structure and the predictions from a model. Among different initial choices, these procedures need to establish a set of representative parameters to be updated in which some are in real error and some are not. It is therefore important to select the correct properties that have to be updated to ensure that no marginal corrections are introduced. In this paper the standard localization criteria are presented and a technique to separate the global localization criteria in family-based criteria for damped structures is introduced. The methods are analyzed and applied to both numerical and experimental examples; a clear enhancement of the results is noticed using the family-based criteria. A simple way to qualify the stability of a localization method to noise is presented.

The yeast UME5 gene regulates the stability of meiotic mRNAs in response to glucose

1994 ◽  
Vol 14 (5) ◽  
pp. 3446-3458
Author(s):  
R T Surosky ◽  
R Strich ◽  
R E Esposito
Keyword(s):  
Vegetative Growth ◽  
Signal Transduction Pathway ◽  
Kinase Domain ◽  
Specific Protein ◽  
Transcript Stability ◽  
The Family ◽  
Two Factors ◽  
Genetic Epistasis ◽  
The Stability ◽  
Acetate Medium

We reported previously that early meiotic transcripts are highly unstable. These mRNAs exhibit half-lives of approximately 3 min when expressed during vegetative growth in glucose medium and are stabilized twofold during sporulation in acetate medium. Two genes, UME2 and UME5, that regulate the stability of meiosis-specific transcripts have been identified. The wild-type UME5 gene, which has been analyzed in detail, decreases the stability of all meiotic mRNAs tested approximately twofold when expressed during vegetative growth but has no effect on the half-lives of a number of vegetative mRNAs examined. The UME5 gene is dispensable for mitotic and meiotic development. Cells in which the entire UME5 gene has been deleted are viable, although the generation time is slightly longer and sporulation is less efficient. The UME5 transcript is constitutively expressed, and its stability is not autoregulated. The UME5 gene encodes a predicted 63-kDa protein with homology to the family of CDC28 serine/threonine-specific protein kinases. The kinase activity appears to be central to the function of the UME5 protein, since alteration of a highly conserved amino acid in the kinase domain results in a phenotype identical to that of a ume5 deletion. Genetic epistasis studies suggest that the UME2 and UME5 gene products act in the same pathway to regulate meiotic transcript stability. This pathway is independent of deadenylation and translation, two factors known to be important in regulating mRNA turnover. Significantly, the UME5-mediated destabilization of meiotic mRNAs occurs in glucose- but not in acetate-containing medium. Thus, the UME5 gene appears to participate in a glucose signal transduction pathway governing message stability.

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