We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order integro-differential equation which mimics a spring-like problem. We determine the potential energy, the rate of change of the kinetic energy of this system, and show that is self-oscillating.
AbstractThis study investigated the effect of cadmium (Cd) chloride on the uptake of N, P, and K and evaluate the effect of Cd-resistant bacterium “N3” on reducing the adverse effect of Cd in grafted and nongrafted plants. The shoot and total dry weights of the nongrafted muskmelon plants decreased under 50 and 100 µM Cd treatments. The scion and shoot dry weights of the grafted plants increased significantly, whereas their root dry weight increased by nearly onefold compared with those of the CK-grafted plants regardless of Cd concentration. The N, P, and K contents in the nongrafted plants decreased under Cd treatments but increased under 50 µM Cd treatment when inoculated with “N3”. The N, P, and K contents in the grafted plants were lower than those treated with only Cd. The grafted and nongrafted plants exhibited low Cd accumulation in the scion or shoot part compared with the root tissues. “N3” inoculation reduced the Cd concentration in all tissues of the grafted and nongrafted plants. Our results demonstrated great variation in Cd accumulation in the grafted and nongrafted muskmelon plants, thereby promoting food safety under Cd contamination conditions.
This article briefly introduces the generalized Lorenz systems family, which includes the classical Lorenz system and the relatively new Chen system as special cases, with infinitely many related but not topologically equivalent chaotic systems in between.
The conditional Lyapunov exponent is defined for investigating chaotic synchronization, in particular complete synchronization and generalized synchronization. We find that the conditional Lyapunov exponent is expressed as a formula in terms of ergodic theory. Dealing with this formula, we find what factors characterize the conditional Lyapunov exponent in chaotic systems.
The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.
By coupling counter--rotating coupled nonlinear oscillators, we observe a ``mixed'' synchronization between the different dynamical variables of the same system. The phenomenon of amplitude death is also observed. Results for coupled systems with co--rotating coupled oscillators are also presented for a detailed comparison. Results for Landau-Stuart and Rossler oscillators are presented.
We present a numerical method for calculation of Ruelle-Pollicott resonances of dynamical systems. It constructs an effective coarse-grained propagator by considering the correlations of multiple observables over multiple timesteps. The method is compared to the usual approaches on the example of the perturbed cat map and is shown to be numerically efficient and robust.
J. K. Bhattacharjee, Debabrata Dutta, Amartya Sarkar
We show that the Lindstedt-Poincare perturbation theory is always a reliable technique in the region of small coupling constant. The harmonic balance result, on the other hand, if expanded in the perturbation parameter may lead to incorrect results.
This paper analyzes the use of the logistic map for cryptographic applications. The most important characteristics of the logistic map are shown in order to prove the inconvenience of considering this map in the design of new chaotic cryptosystems.
An outline of theoretical estimates is given regarding the dependence of the value of the diffusion coefficient $D$ on the size $R$ of the remainder of the normal form in doubly or simply resonant domains of the action space of 3dof Hamiltonian systems.
Many libraries have expressed an interest in the possibility of using CD‐ROM to provide an interactive public access catalogue, as an alternative to fiche‐based products and to providing online access to the networked library system. Similarly, many systems suppliers have included CD‐ROM in their list of future developments. However, to date in the UK, there have been few moves to introduce CD‐ROM‐based library catalogues. One of the first library systems' suppliers to provide a CD‐ROM product is CLSI; as with all CD‐ROM products, it has found its first users in the US market, though it is available to all CLSI customers. In the US, libraries have turned to CD‐ROM sometimes as an interim solution between manual or fiche catalogues and an integrated online public catalogue or, sometimes, when the multi‐site nature of the organisation or cooperation between library organisations made a union catalogue necessary. In these cases, the enhanced and interactive searching available on CD‐ROM made it a preferable option to fiche or other passive catalogue forms. This article does not discuss the feasibility of CD‐ROM for library catalogues; these arguments have been covered elsewhere, for example in the report by John Akeroyd et al to the British Library Research & Development Department. This article is a purely descriptive account of one commercial product which happens to be the first available in the UK aimed specifically at providing an interface similar to that available on an OPAC. In this instance the OPAC in question is CL‐CAT; CD‐CAT emulates the facilities and searching available on CLSI's online CL‐CAT, but takes advantage of the power of the CD workstation (the PC) to make greater use of features such as windows, colour and output to print files.
We quantitatively investigate the violations of local equilibrium in the $φ^4$ theory under thermal gradients, using stochastic thermostats. We find that the deviations from local equilibrium can be quite well described by a behavior $\sim(\nabla T)^2$. The dependence of the quantities on the thermostat type is analyzed and its physical implications are discussed.
The authors investigate the impact of external sources on the pattern formation of concentration profiles of passive tracers in a two-dimensional shear flow. By using the pullback attractor technique for the associated nonautonomous dynamical system, it is shown that a unique time-almost periodic concentration profile exists for time-almost periodic external source.
A dynamic equation for velocity structure functions $S_{n}(r) = <(u(x)-u(x'))^{n}>$ in strong turbulence is derived in the one-loop (eddy viscosity) approximation. This homogemeous differential equation yields scaling exponents $ξ_{n}$ in the relations $S_{n}(r)\propto r^{ξ_{n}}$ which are in a very good agreement with experimental data.
Accumulation point of period-tripling bifurcations for complexified Henon map is found. Universal scaling properties of parameter space and Fourier spectrum intrinsic to this critical point is demonstrated.
A method of expansion of solutions of singularly perturbed nonlinear systems in power series of small parameters is applied to the popular Lorenz model in synergetics.Simple asymptotic expressions for the solution to the model in consideration is obtained for some extreme cases.The times for achieving of quasistationary and stationary states are estimated.
Wave functions of plane polygonal billiards are investigated. It is demonstrated that they have clear structures (superscars) related with families of classical periodic orbits which do not disappear at large energy.
Statistics of Poincar\' e recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the statistics of the return times.
The lectures are centered around three selected topics of quantum chaos: the Selberg trace formula, the two-point spectral correlation functions of Riemann zeta function zeros, and of the Laplace--Beltrami operator for the modular group. The lectures cover a wide range of quantum chaos applications and can serve as a non-formal introduction to mathematical methods of quantum chaos.