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Home  >  Transactions of NAMP VOL.12

27. SUSTAINED OSCILLATION IN SOLUTIONS OF LINEAR PIECEWISE CONTINUOUS ORDINARY DELAY INTEGRO DIFFERENTIAL EQUATION BY BROWNIAN WHITE NOISE by Augustine Omoghaghare Atonuje and Newton I.Okposo Volume 12, (July – Sept., 2020 Issue)
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SUSTAINED OSCILLATION IN SOLUTIONS OF LINEAR PIECEWISE CONTINUOUS ORDINARY DELAY INTEGRO-DIFFERENTIAL EQUATION BY BROWNIAN WHITE NOISE
Augustine Omoghaghare Atonuje and Newton I.Okposo
Department of Mathematics, Delta State University, Abraka, Nigeria.
Abstract
The paper studies the oscillatory behavior of the solution of a linear piece-wise continuous deterministic ordinary delay integro-differential equation with time lags. The system is disturbed by an Ito-type Brownian white noise to form a stochastic delay integro-differential equation (SDIDE). Although, it is a known fact that oscillation in solutions of deterministic ordinary delay differential equations is solely caused by the existence of time delays, it is established in this note that even if the deterministic system, in which the noise is absent allows a non-oscillatory solution, the presence of noise in the stochastic delay integro-differential equation will continue to sustain oscillation.
Keywords: Oscillation, piece-wise continuous, deterministic integro-differential equation, time lags, Brownian white noise, stochastic delay integro-differential equations.
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