In this paper, we investigate the population dynamics of phytoplankton–zooplankton–nanoparticle model with diffusion and density dependent death rate predator. The functional response predator in is considered as Beddington–DeAngelis type. stability analysis equilibrium points observed by applying Routh–Hurwitz criterion. Numerical simulations are given to illustrate theoretical results.

Abstract In this paper, We first propose a systematic modeling of the wheeled mobile manipulator built from a robotic arm mounted on a wheeled mobile platform by using Lagrange dynamics equation and nonholonomic dynamics Routh equation. Then we use artificial potential field as part of feedback to accomplish the wheeled mobile manipulator’s motion planning, and its stability is guaranteed by Ly...

We show that L 4 and L 5 in the spatial restricted circular three{body problem are Nekhoroshev{ stable for all but a few values of the reduced mass up to the Routh critical value. This result is based on two extensions of previous results on Nekhoroshev{stability of elliptic equilibria, namely to the case of`directional quasi{convexity', a notion introduced here, and to a (non-convex) steep cas...

In the present manuscript, an investigation on synchronization, anti -synchronization and hybridsynchronization behavior of a double pendulum under the effect of external forces using active control technique based on the Lyapunov stability theory and the Routh-Hurwitz criteria, have been made. The designed controller with a new choice of co-efficient matrix of the error-dynamics are found to b...

In this paper, the circulatory integral and Routh?s equations of Lagrange systems are established with Riemann-Liouville fractional derivatives, is obtained by making use relationship between integrals derivatives. Thereafter, given based on integral. Two examples presented to illustrate application results.

Beginning with Hermite’s integral representation of the Hurwitz zeta function, we derive explicit expressions in terms of elementary, polygamma, and negapolygamma functions for several families of integrals of the type ∫∞ 0 f(t)K(q, t)dt with kernels K(q, t) equal to ( e2πqt − 1 )−1 , ( e2πqt + 1 )−1 , and (sinh(2πqt))−1.

Hunting; Rail wheelset; Hopf bifurcation; Discontinuous nonlinearity; Routh–Hurwitz criterion; Equivalent function; Analytical approach. Abstract This paper presents an investigation on bifurcation of railway bogie behavior in the presence of nonlinearities which are yaw damping forces in longitudinal suspension system and the friction creepage model of thewheel/rail contact including clearance...

In the film formation of latex, particle deformation can occur by processes of wet sintering, dry sintering, or capillary action. When latex films dry nonuniformly and when particles deform and coalesce while the film is still wet, a detrimental skin layer will develop at the film surface. In their process model, Routh and Russel proposed that the operative particle deformation mechanism can be...

Stability analysis in compliant mechanism (CM) design is of utmost importance. From a practical point of view, a CM that is unstable is of no significance (has no practical value). Three useful plots were considered in the evaluation of each of the dynamic models of nine configurations of compliant constant-force compression mechanisms (CCFCMs) for their stability characteristics, which include...