Nonlinear dynamical wave structures to the Zoomeron equation for population models

In this paper, the nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achevied for the first time in the framwork of the Paul-Painlevé approachmethod (PPAM). When the variables appearing in the exact solutions take specific values, the solaitry wave solutions will be easily satisfied.The realized results prove the efficiency of this technique.

Stability Analysis of Pressure and Penetration Rate in Rotary Drilling System

The purpose of this paper is to stabilize the annular pressure profile throughout the wellbore continuously while drilling. A new nonlinear dynamical system is developed and a controller is designed to stabilize the annular pressure and achieve asymptotic tracking by applying feedback control of the main pumps. Hence, the paper studies the control design for the well known Managed Pressure Drilling system (MPD). MPD provides a closedloop drilling process in which pore pressure, formation fracture pressure, and bottomhole pressure are balanced and managed at the surface. Although, responses must provide a solution for critical downhole pressures to preserve drilling efficiency and safety. Our MPD scheme is elaborated in reference to a nontrivial backstepping control procedure and the effectiveness of the proposed control laws are shown by simulations.

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Nonlinear Dynamical Systems for Malaria Transmission and Control: Ross-Macdonald Model

Malaria was declared an emergency in Nigeria and strategies for the control of Malaria in Nigeria were adopted to reduce its prevalence to a level at which the disease will no longer constitute public health problems. In this work, we presented a deterministic (Ross–Macdonald model susceptible, expose/ infected, infectious and recovered) model incorporating the method of control adopted by national Malaria and leprosy control program. We established the disease free and the endemic equilibrium states and carried out the stability analysis of the disease. Free and the equilibrium state. We also carried out numerical simulation of the model to have an insight into the dynamics of the model. We found out that the disease free equilibrium state is stable. The feedback dynamics from mosquito to human and back to mosquito involve considerable time due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a Ross–Macdonald model. The Jacobiant results showed that it would be very difficult to completely eradicate Malaria from Nigeria using the method adopted by national Malaria and leprosy control program.

Dynamical systems implementation of intrinsic sentence meaning

This paper proposes a model for implementation of intrinsic natural language sentence meaning in a physical language understanding system, where 'intrinsic' is understood as 'independent of meaning ascription by system-external observers'. The proposal is that intrinsic meaning can be implemented as a point attractor in the state space of a nonlinear dynamical system with feedback which is generated by temporally sequenced inputs. It is motivated by John Searle's well known (1980) critique of the then-standard and currently still influential Computational Theory of Mind (CTM), the essence of which was that CTM representations lack intrinsic meaning because that meaning is dependent on ascription by an observer. The proposed dynamical model comprises a collection of interacting artificial neural networks, and constitutes a radical simplification of the principle of compositional phrase structure which is at the heart of the current standard view of sentence semantics because it is computationally interpretable as a finite state machine.

Averaging method and two-sided bounded solutions on the axis of systems with impulsive effects at non-fixed times

The averaging method, originally offered by Krylov and Bogolyubov for ordinary differential equations, is one of the most widespread and effective methods for the analysis of nonlinear dynamical systems. Further, the averaging method was developed and applied for investigating of various problems. Impulsive systems of differential equations supply as mathematical models of objects that, during their evolution, they are subjected to the action of short-term forces. Many researches have been devoted to non-fixed impulse problems. For these problems, the existence, stability, and other asymptotic properties of solutions were studied and boundary value problems for impulsive systems were considered. Questions of the existence of periodic and almost periodic solutions to impulsive systems also were examined. In this paper, the averaging method is used to study the existence of two-sided solutions bounding on the axis of impulse systems of differential equations with non-fixed times. It is shown that a one-sided, bounding, asymptotically stable solution to the averaged system generates a two-sided solution to the exact system. The closeness of the corresponding solutions of the exact and averaged systems both on finite and infinite time intervals is substantiated by the first and second theorems of N.N. Bogolyubov.