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Transition from chaotic to ordered state has been observed during the initial stage of a discharge in a cylindrical DC glow discharge plasma. Initially it shows a chaotic behavior but increasing the discharge voltage changes the characteristics of the discharge glow and shows a period subtraction of order 7 period → 5 period → 3 period → 1 period, i.e. the system goes to single mode through odd cycle...
Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The monochromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
The Macintosh application StdMap allows easy exploration of many of the phenomena of area-preserving mappings. This tutorial explains some of these phenomena and presents a number of simple experiments centered on the use of this program.
We wish to report the occurrence of vibrational resonance in certain discrete systems like sine square map and sine circle map, in a unique fashion, comprising of multiple resonant peaks which pave the way for enrichment. As the systems of our choice are capable of exhibiting vibrational resonance behaviour unlike the earlier reports, they are taken for investigation and the necessary numerical and...
A large number of studies have recently been carried out on the early signatures of regime shifts in a number of dynamical systems, e.g., ecosystems, the climate, fish and wildlife populations, financial markets, complex diseases and gene circuits. The underlying model in most cases is that of the fold-bifurcation in which a sudden regime shift occurs at a bifurcation point. The shift involves a discontinuous...
The paper presents bifurcation behaviour of a single-phase induction motor. Study of bifurcation of a system gives the complete picture of its dynamical behaviour with the change in system’s parameters. The system is mathematically described by a set of differential equations in the state space. Induction motors are very widely used in domestic and commercial applications. Single-phase capacitor-run...
In this paper, a generalized scheme is proposed for designing multistable continuous dynamical systems. The scheme is based on the concept of partial synchronization of states and the concept of constants of motion. The most important observation is that by coupling two m-dimensional dynamical systems, multistable nature can be obtained if i number of variables of the two systems are completely synchronized...
In this paper, the classical problem of the motion of a particle in one dimension with an external time-dependent field is studied from the point of view of the dynamical system. The dynamical equations of motion of the particle are formulated. Equilibrium points of the non-oscillating systems are found and their local stability natures are analysed. Effect of oscillating potential barrier is analysed...
In this paper we report a time-delayed chameleon-like chaotic system which can belong to different families of chaotic attractors depending on the choices of parameters. Such a characteristic of self-excited and hidden chaotic flows in a simple 3D system with time delay has not been reported earlier. Dynamic analysis of the proposed time-delayed systems are analysed in time-delay space and parameter...
Quantum analogue of stabilised forced oscillations around an unstable equilibrium position is explored by solving the non-stationary Schrödinger equation (NSE) of the inverted harmonic oscillator (IHO) driven periodically by spatial uniform field of frequency $$\Omega $$ Ω , amplitude $$F_{0}$$ F0 and phase $$\phi $$ ϕ , i.e. the system with the Hamiltonian of $$\hat{{H}}=(\hat{{p}}^{2}/2m)-(m\omega...
The main thrust of this paper is to consider a delayed q-deformed discrete susceptible–infected–susceptible (SIS) epidemic model. Parametric conditions on the local stability of the disease-free fixed point and the endemic fixed points are obtained. A codimension-one bifurcation analysis at the fixed points of the model is discussed. The model has a variety of bifurcations such as flip, transcritical,...
This work studies a forced generalised Liénard oscillator with $$\phi ^8$$ ϕ8 potential with order 8 dissipation. The fixed points and their stability have been analysed for autonomous and non-dissipative Liénard oscillator. The system can exhibit three, five or seven fixed points and the corresponding stability diagram is checked and analysed. The effect of restoring parameters on the potential...
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