Vol. 5, No. 2 (2016): Regular Issue

The global dynamics of a continuum rotor excited by nonlinear oilfilm force and electromagnetic force is investigated. The governing equation of the system is obtained using the Galerkin’s method. The dynamical systems are reduced into two 2-dimensional systems in Yand Z-directions. The analytical conditions for global transversality and tangency to the separatrix are presented. The global and local dynamics of the system is determined through the G-function and G(1)-function and is compared to numerical solution. The periodicity of periodic flow of the rotor is determined by the L-function. The complexity of the nonlinear continuum rotor system is demonstrated through global transversality and tangency of the periodic motions to separatrix.

In this work, we investigate the global relative controllability of nonlinear neutral fractional Volterra integrodifferential systems with multiple delays. Controllability criteria for nonlinear fractional order systems are established. The results are obtained by using the Schauder fixed point theorem. Moreover, some numerical examples are provided to illustrate the effectiveness and applicability of the proposed criteria.

A model with hyperchaos is studied by means of Lyapunov twoparameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the parameter plane of coupled systems, corresponding to the cases of interaction of quasiperiodic and hyperchaotic subsystems.

Impact oscillators are found in many applications. It is common for these applications to undergo the inadvertent state of grazing bifurcation. Vibro-impact incited grazing and route-to-chaos are difficult to control. The Newtonian model of a vibro-impact system rich of complex nonlinear behaviors is considered for the mitigation of impact induced instability and grazing. A novel concept capable of simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain is adopted to formulate a viable control solution. The concept has been demonstrated to be feasible for the control of dynamic instability including bifurcation and route-to-chaos in many nonlinear systems. The developed controller explores wavelet adaptive filters and filtered-x least mean square algorithm to the successful moderation of the grazing and dynamic instability of the non-smooth system. The qualitative behavior of the controlled impact oscillator follows a definitive fractal topology before settling into a stable manifold. The controlled response is categorically quasi-periodic and of the prescribed vibration amplitude and frequency spectrum.

We investigate the dynamical system generated by the floor function λx defined on R and with a parameter λ ∈ R. For each given m ∈ N we show that there exists a region of values of λ, where the floor function has exactly m fixed points (which are non-negative integers), also there is another region for λ , where there are exactly m+1 fixed points (which are non-positive integers). Moreover the full set Z of integer numbers is the set of fixed points iff λ = 1. We show that depending on λ and on the initial point x the limit of the forward orbit of the dynamical system may be one of the following possibilities: (i) a fixed point, (ii) a two-periodic orbit or (iii) ±ꝏ.

we study a system of two linear oscillators coupled to a k-order nonlinear oscillator with a mass much smaller than the mass of the linear oscillators. We prove that the Slow Invariant Manifold of the system may bifurcate only when the order of the nonlinear oscillator is an odd number.

The present article deals with the influence of a constant proportion of prey refuge in presence of intra-specific competition among predator population of a prey-dependent three species food chain model. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. The preliminary results such as boundedness and dissipativeness of the system are established. Stability analysis including local and global stability of the equilibria has been carried out in order to examine the behaviour of the system. The present system experiences Hopf-Andronov bifurcation for suitable choice of the parameter values. The influences of the prey refuge parameters on the dynamical behaviour of the system are exhibited through several plots and discussed at some equilibrium positions. It is worth-noting that prey refuge has stabilization effect in some selected situations and bears the potential to control chaotic dynamics of the system. Hence, prey refuge may be of some use for biological control mechanism. Numerical simulations are performed to validate the applicability of the model under consideration.

This paper investigates the random rattle motion of a single stage spur gear pair subjected to deterministic and random excitation. The motion is treated separately as free flight between the boundaries and the instant impact at the two boundaries. Numerical path integration method is applied to obtain the probability density of the response during free flight. Monte Carlo simulation is also conducted to verify the efficiency and accuracy of path integration in solving this strongly nonlinear dynamic problem. Comparison between results from path integration and Monte Carlo simulation is made and good agreement is achieved.

Magnetic fluid is a new type of functional material. The motion of com-pressible, viscous self-gravitating fluids can be expressed by Navier-Stokes-Poisson equations. This study demonstrates the global, non-vacuum solutions with large amplitude to the initialboundary value problem of the one-dimensional compressible Navier- Stokes-Poisson system with degenerate dependent viscosity coefficients and density and temperature dependent heat conductivity coefficients. The main constituent of the detail analysis is to derive the positive lower and upper bounds on the specific volume and the absolute temperature.