The paper confronts chaos indicators of two basic types: spectral methods and variational methods. The spectral methods include the spectral numbers and the integrated autocorrelation function. Variational methods discussed are FLI, MEGNO and OFLI2. Using an ad hoc model of coupled pendulum we demonstrate various spurious patterns that appear in the maps of the chaos indicators. Spectral method...

For mobile <span>communication and spatial detection of antennas should have high directive radiation pattern, in this context pattern synthesis planar circular antenna arrays is highly significant such design has been done inverse weed optimization. The basic objective e to study invasive optimization compression with modified chaotic adaptive focus the effect factors suitable for sinuso...

In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the laminar flow, one notes a a qualitative change in its lifetime, from smoothly varying and short one on the laminar side to sensitively dependent on initial cond...

A fractal method to detect, locate and quantify chaos in multidimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used to analyse both classical and relativistic Hamiltonian systems of more than two degrees of freedom. As an application of the method we study a couple of two ...

We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic underlying classical dynamics, and for each case the limiting distribution is universal (system independent). Thus, a new criterion for quantum chaos is provided b...

We study a class of two-sector endogenous growth models in the presence of a positive external effect. The class of models exhibits global indeterminacy of equilibria. The qualitative properties of a set of examples are analyzed by means of analytical and numerical methods. We also construct robust examples of both topological and ergodic chaos. Journal of Economic Literature Classification Num...

It is shown that three-dimensional dissipative quadratic systems of ordinary differential equations with a total of four terms on the right-hand side of the equations do not exhibit chaos. This complements recent work of Sprott who has given many examples of chaotic quadratic systems with as few as five terms on the right-hand side of the equations. AMS classification scheme numbers: 34C99, 34O...

We study, in two space dimensions, the collective properties of constant-speed polar point particles interacting locally by nematic alignment in the presence of noise. This minimal approach to self-propelled rods allows one to deal with large numbers of particles, which exhibit a rich phenomenology distinctively different from all other known models for self-propelled particles. Extensive simul...

Statistical behavior of a classical φ4 Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitions to equipartitions, and the scaling beha...

Using a variant of the interpolating Hamiltonian technique, we show that there exists, in the Sherrington-Kirkpatrick spin glass, an exact connection between the sample-to-sample fluctuations of the free energy and bond chaos involving 2and 4-replica overlaps between replicas with different but correlated bonds. This relation is used to derive an upper bound of the fluctuations. PACS numbers: 7...