混沌动力学
We analyse the asymptotic growth of the error for Hamiltonian flows due to small random perturbations. We compare the forward error with the reversibility error, showing their equivalence for linear flows on a compact phase space. The…
We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a…
Shannon Entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs…
It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime…
Weak noise smooths out fractals in a chaotic state space and introduces a maximum attainable resolution to its structure. The balance of noise and deterministic stretching/contraction in each neighborhood introduces local invariants of the…
Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much…
The Chua's circuit is a paradigm for nonlinear scientific studies. It is usually simulated by means of numerical methods under IEEE 754-2008 standard. Although the error propagation problem is well known, little attention has been given to…
The Y-chromosome degeneration is still an intriguing mechanism and comprises the very origin of sex. We present a coupled version of the well known logistic map and the logistic equation describing the evolution of XY chromosomes. Although…
We propose a noble physical model obtained from a Hamiltonian with periodic potential. This model is canonical, reversible and brings about chaotic superdiffusion with energy fluctuation divergence. The analytical formula of invariant…
Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness and hence the complexity of the state time series…
We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz-63 attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear…
The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The…
The quasiperiodic route to chaos in a piecewise linear forced parallel LCR circuit with a negative conductance and diode is studied analytically. An explicit analytical solution for the normalized state equations of the piecewise linear…
Along with widely used numerical methods for estimating and computing the Lyapunov dimension there is an effective analytical approach, proposed by G.A. Leonov in 1991. The Leonov method is based on the direct Lyapunov method with special…
Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's…
We report the existence of diverse routes of transition from amplitude death (AD) to oscillation death (OD) in three different diffusively coupled systems, those are perturbed by a symmetry break- ing repulsive coupling link. For limit…
We investigated experimentally the short- and long-range correlations in the fluctuations of the resonance frequencies of flat, rectangular microwave cavities that contained antennas acting as point-like perturbations. We demonstrate that…
Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…
Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three reciprocally coupled…
We discuss recent work with E.Floratos (JHEP 1004:036,2010) on Nambu Dynamics of Intersecting Surfaces underlying Dissipative Chaos in $R^{3}$. We present our argument for the well studied Lorenz and R\"{o}ssler strange attractors. We…