Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex dynamical properties of coupled Van der Pol-Duffing oscillators
  with balanced loss and gain   We consider a Hamiltonian system of coupled Van der Pol-Duffing(VdPD)
oscillators with balanced loss and gain. The system is analyzed perturbatively
by using Renormalization Group(RG) techniques as well as Multiple Scale
Analysis(MSA). Both the methods produce identical results in the leading order
of the perturbation. The RG flow equation is exactly solvable and the slow
variation of amplitudes and phases in time can be computed analytically. The
system is analyzed numerically and shown to admit periodic solutions in regions
of parameter-space, confirming the results of the linear stability analysis and
perturbation methods. The complex dynamical behavior of the system is studied
in detail by using time-series, Poincar$\acute{e}$-sections, power-spectra,
auto-correlation function and bifurcation diagrams. The Lyapunov exponents are
computed numerically. The numerical analysis reveals chaotic behaviour in the
system beyond a critical value of the parameter that couples the two VdPD
oscillators through linear coupling, thereby providing yet another example of
Hamiltonian chaos in a system with balanced loss and gain. Further, we modify
the nonlinear terms of the model to make it a non-Hamiltonian system of coupled
VdPD oscillators with balanced loss and gain. The non-Hamiltonian system is
analyzed perturbativly as well as numerically and shown to posses regular
periodic as well as chaotic solutions. It is seen that the
${\cal{PT}}$-symmetry is not an essential requirement for the existence of
regular periodic solutions in both the Hamiltonian as well as non-Hamiltonian
systems.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg