Generalized Stability Theorem for Non-autonomous Differential Equation with Application

2015 ◽  
Author(s):  
Mei Zhang ◽  
Lequan Min ◽  
Xiuping Yang
Keyword(s):  
Differential Equation ◽  
Stability Theorem ◽  
Generalized Stability

scholarly journals A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Mei Zhang ◽  
Danling Wang ◽  
Lequan Min ◽  
Xue Wang
Keyword(s):  
Discrete Time ◽  
Chaotic Map ◽  
Stability Theorem ◽  
Pseudorandom Number Generator ◽  
Generalized Synchronization ◽  
Key Space ◽  
Chaos System ◽  
Definition Of ◽  
Study Designs ◽  
Generalized Stability

Firstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES) in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.

scholarly journals Fixed points and stability in nonlinear neutral integro-differential equations with variable delay

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 781-795
Author(s):  
Imene Soualhia ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Initial Function ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Stability Theorem ◽  
Variable Delay ◽  
Necessary And Sufficient

The nonlinear neutral integro-differential equation x'(t) = -?t,t-?(t) a (t,s) g(x(s))ds+c(t)x'(t-?(t)), with variable delay ?(t) ? 0 is investigated. We find suitable conditions for ?, a, c and g so that for a given continuous initial function ? mapping P for the above equation can be defined on a carefully chosen complete metric space S0? in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient conditions. The obtained theorem improves and generalizes previous results due to Burton [6], Becker and Burton [5] and Jin and Luo [16].

New stability theorem for uncertain pantograph differential equations

2021 ◽  
Vol 40 (5) ◽  
pp. 9403-9411
Author(s):  
Zhifu Jia ◽  
Xinsheng Liu ◽  
Yu Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Stability Theorem ◽  
Sufficient Condition ◽  
Stability In Distribution ◽  
Delay Differential

Uncertain pantograph differential equation (UPDE for short) is a special unbounded uncertain delay differential equation. Stability in measure, stability almost surely and stability in p-th moment for uncertain pantograph differential equation have been investigated, which are not applicable for all situations, for the sake of completeness, this paper mainly gives the concept of stability in distribution, and proves the sufficient condition for uncertain pantograph differential equation being stable in distribution. In addition, the relationships among stability almost surely, stability in measure, stability in p-th moment, and stability in distribution for the uncertain pantograph differential equation are also discussed.

scholarly journals Generalized Stability of Euler-Lagrange Quadratic Functional Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hark-Mahn Kim ◽  
Min-Young Kim
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
General Solution ◽  
Rational Numbers ◽  
Stability Theorem ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Generalized Stability

The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equationf(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in(β,p)-Banach space, wherea,bare fixed rational numbers such thata≠-1,0andb≠0.

scholarly journals A Stability theorem for the nonlinear differential equation x″+p(t)g(x)h(x′) = 0

1969 ◽  
Vol 10 (1-2) ◽  
pp. 169-172 ◽  
Author(s):  
A. G. Kartsatos
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Stability Theorem ◽  
Image Position ◽  
Derivatives Of

K. W. Chang generalizing a result of Lazer [3], proved in [4] the following THEOREM 1. Suppose that f:I → R+ = (0, + ∞), I = ([t0, + ∞), t0 0, is a non-decreasing function whose derivatives of orders ≧ 3 exist are continuous on ([t0, + ∞). Moreover, limt→+∞f(t) = +∞ and for some α, 1≧ α ≧ 2, and F =f-1/α then every solution x(t) of the equation tends to zero as t - + ∞.

scholarly journals Asymptotic Stability of Neutral Set-Valued Functional Differential Equation by Fixed Point Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Junyan Bao ◽  
Peiguang Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Asymptotic Stability ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Stability Theorem ◽  
Point Method ◽  
Functional Differential ◽  
Necessary And Sufficient

This paper studies a class of nonlinear neutral set-valued functional differential equations. The globally asymptotic stability theorem with necessary and sufficient conditions is obtained via the fixed point method. Meanwhile, we give an example to illustrate the obtained result.

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