Relaxed Control for a Class of Strongly Nonlinear Impulsive Evolution Equations

Two widely used concepts in physics and the life sciences are combined: mean field theory and time-discrete time series modeling. They are merged within the framework of strongly nonlinear stochastic processes, which are processes whose stochastic evolution equations depend self-consistently on process expectation values. Explicitly, a generalized autoregressive (AR) model is presented for an AR process that depends on its process mean value. Criteria for stationarity are derived. The transient dynamics in terms of the relaxation of the first moment and the stationary response to fluctuations in terms of the autocorrelation function are discussed. It is shown that due to the stochastic feedback via the process mean, transient and stationary responses may exhibit qualitatively different temporal patterns. That is, the model offers a time-discrete description of many-body systems that in certain parameter domains feature qualitatively different transient and stationary response dynamics.

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Impulsive Evolution Equations and Population Models

Dynamics of Complex Interconnected Biological Systems ◽

10.1007/978-1-4684-6784-0_10 ◽

1990 ◽

pp. 175-203 ◽

Cited By ~ 1

Author(s):

Phil Diamond

Keyword(s):

Evolution Equations ◽

Population Models ◽

Impulsive Evolution Equations

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On the stability of first order impulsive evolution equations

Opuscula Mathematica ◽

10.7494/opmath.2014.34.3.639 ◽

2014 ◽

Vol 34 (3) ◽

pp. 639 ◽

Cited By ~ 14

Author(s):

JinRong Wang ◽

Michal Fečkan ◽

Yong Zhou

Keyword(s):

Evolution Equations ◽

First Order ◽

The Stability ◽

Impulsive Evolution Equations

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A Study on Impulsive Hilfer Fractional Evolution Equations with Nonlocal Conditions

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0015 ◽

2020 ◽

Vol 21 (2) ◽

pp. 205-218

Author(s):

Haide Gou ◽

Yongxiang Li

Keyword(s):

Fractional Derivative ◽

Measure Of Noncompactness ◽

Evolution Equations ◽

Mild Solutions ◽

Nonlocal Conditions ◽

Sobolev Type ◽

Initial Value ◽

Liouville Fractional Derivative ◽

Characteristic Solution Operators ◽

Impulsive Evolution Equations

AbstractIn this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining measure of noncompactness with the fixed-point methods, we obtain the existence results of mild solutions with two new characteristic solution operators. The results we obtained are new and more general to known results. At last, an example is provided to illustrate the results.

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