By applying the Adams-Bashforth-Moulton method (ABM), this paper explores complexity and synchronization of a fractional-order laser dynamical model. The dynamics under variance derivative order q parameters system have examined using multiscale algorithm bifurcation diagram. Numerical simulation outcomes demonstrate that generates chaos with decreasing q. Moreover, designs coupled network syst...

In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM was utilized establish approximate series solutions. technique considered be an extension original Adams–Bashforth–Moulton approach. Numerical simulations and figures are discussed, in order show efficiency of proposed method. futur...

Regenerative chatter is the most important factor affecting stability of milling process. It core for suppressing and improving production efficiency to accurately efficiently identify stable region chatter. Therefore, according theory predictor-corrector, three predictor–corrector methods (PCM) are, respectively, proposed by applying fourth-order Adams-Bashforth-Moulton formula, Simpson Hammin...

We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. first establish existence, uniqueness, non-negativity, boundedness of solutions to confirm biological feasibility model. Moreover, Lyapunov direct method including generalized LaSalle invariance principle is applied investigate global stability prey-free poin...

At the end of November 1914 Lord Moulton (1844-1921) became the director of explosives production in the War Office. A 70-year-old jurist may seem an extraordinary choice, but he was an extraordinary man. He was Senior Wrangler at Cambridge, was elected to the Royal Society for research on electricity, and learned about chemistry as a barrister for dye and explosives manufacturers. He assembled...

In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solv...

How far the stability domain of a numerical method for approximating solutions to differential equations extends along the imaginary axis indicates how useful the method is for approximating solutions to wave equations; this maximum extent is termed the stability ordinate, also known as the imaginary stability boundary. It has previously been shown that exactly half of Adams-Bashforth, Adams-Mo...