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arxiv: 2605.12533 · v1 · pith:W6F5EWKJnew · submitted 2026-05-01 · 📡 eess.SY · cs.SY· nlin.CD

Investigation of Chaotic Behavior in Clapp Oscillator

Ivana Vasiljevi\'c , Nikola Petrovi\'c , Aleksandra Leki\'c This is my paper

Pith reviewed 2026-05-14 21:42 UTC · model grok-4.3

classification 📡 eess.SY cs.SYnlin.CD
keywords chaotic oscillatorClapp oscillatorchaotic radarmicrostrip technologynonlinear dynamicstransistor circuit
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The pith

Suitable parameters turn the Clapp oscillator chaotic while retaining its simple design for radar applications.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper explores chaotic dynamics in Clapp oscillators, which consist of a single transistor along with inductors and capacitors. The Clapp topology is selected for its straightforward design and strong performance characteristics. By identifying appropriate parameter values, the oscillator can enter a chaotic regime. This opens the possibility of using such circuits in chaotic radar systems. The proposed construction method supports experimental testing through microstrip technology.

Core claim

In the Clapp oscillator, which uses one transistor and a small number of reactive components, chaotic behavior arises from specific choices of circuit parameters. The investigation shows an approach to construct this chaotic oscillator. The resulting device preserves the original simplicity and can serve as the basis for chaotic radar. Experimental confirmation is feasible using microstrip fabrication techniques.

What carries the argument

The Clapp oscillator with tuned parameters to trigger chaotic regime through its inherent nonlinearity.

Load-bearing premise

Suitable parameter choices exist that reliably induce chaotic dynamics in the Clapp topology while preserving its design simplicity and performance.

What would settle it

Simulation results or physical measurements that fail to show any chaotic behavior, such as a strange attractor, for any tested parameter set in the Clapp circuit would disprove the investigated approach.

Figures

Figures reproduced from arXiv: 2605.12533 by Aleksandra Leki\'c, Ivana Vasiljevi\'c, Nikola Petrovi\'c.

Figure 1
Figure 1. Figure 1: Clapp oscillator [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Obtained parameters for the BJT large signal model, as in equation (1), are I S  47.1 pA and   0.7894 . B. Clapp oscillator circuit parameters The Clapp oscillator is constructed using transistor BFU730F. For the supply voltage of VCC 12 V , biasing resistors 1 R  5 k and 2 R  7 k , and emitter resistance 500 RE  , capacitors and inductor in the circuit are chosen to operate at the resonant frequ… view at source ↗
Figure 3
Figure 3. Figure 3: Time diagrams of the Clapp oscillator operating in chaos. [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Dependence one of the state variables with respect to another in the Clapp oscillator operating in chaos. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Dependance of the Jacobian’s maximum eigenvalue on [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
read the original abstract

In this paper we investigate the chaotic behavior of the class of oscillators denoted as Clapp oscillators. Clapp oscillator is a simple oscillator containing one transistor and a few reactive elements - inductors and capacitors. This oscilllator is chosen for its design simplicity and a good performance. Oscillator with chaotic behavior can be used to construct chaotic radar. For that matter, in this paper is investigated approach for construction of the chaotic Clapp oscillator, which can be further verified experimentally using microstrip technology.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript claims to investigate chaotic behavior in Clapp oscillators, a simple single-transistor circuit with a few reactive elements chosen for design simplicity and performance. It asserts that an approach for constructing a chaotic Clapp oscillator has been investigated, which can be further verified experimentally using microstrip technology for applications such as chaotic radar.

Significance. If the claimed investigation were supported by explicit models, parameter choices, simulations, or analysis demonstrating reliable chaos while preserving the topology's simplicity, the result could contribute to practical chaotic signal generation for radar systems. The current manuscript, however, contains no such supporting material.

major comments (2)
  1. [Abstract] Abstract: The claim that 'an approach for construction of the chaotic Clapp oscillator' is investigated is unsupported; the text supplies neither circuit equations, bias conditions, component values, nor any dynamical analysis (e.g., Lyapunov spectra, bifurcation diagrams, or numerical integration results) to establish the existence or controllability of chaos.
  2. [Full text] Full manuscript: The description is limited to the standard single-transistor Clapp topology; no modifications, parameter tuning strategy, or verification that chaos can be induced without compromising the oscillator's design simplicity are provided, rendering the central claim unverifiable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review. We acknowledge that the submitted manuscript is brief and does not yet contain the supporting models, parameters, or dynamical analysis needed to substantiate the claims of chaotic behavior. We will revise the paper accordingly to address these points while preserving the focus on the Clapp oscillator's design simplicity.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that 'an approach for construction of the chaotic Clapp oscillator' is investigated is unsupported; the text supplies neither circuit equations, bias conditions, component values, nor any dynamical analysis (e.g., Lyapunov spectra, bifurcation diagrams, or numerical integration results) to establish the existence or controllability of chaos.

    Authors: We accept the referee's observation. The current manuscript provides only a high-level outline. In the revised version we will derive and present the circuit equations for the Clapp topology, specify bias conditions and component values that produce chaos, and include numerical results such as Lyapunov spectra and bifurcation diagrams obtained via integration to confirm the chaotic regime and its controllability. revision: yes

  2. Referee: [Full text] Full manuscript: The description is limited to the standard single-transistor Clapp topology; no modifications, parameter tuning strategy, or verification that chaos can be induced without compromising the oscillator's design simplicity are provided, rendering the central claim unverifiable.

    Authors: The manuscript intentionally begins with the unmodified single-transistor Clapp circuit to retain its simplicity. The revised full text will explicitly describe the parameter-tuning approach (e.g., adjustment of the series capacitor to drive the system through period-doubling into chaos) and will supply simulation evidence that chaotic operation is achieved without adding components or altering the core topology. revision: yes

Circularity Check

0 steps flagged

No derivation chain or load-bearing steps present; paper is descriptive intent only

full rationale

The manuscript provides only a high-level description of intent to investigate chaotic behavior in the Clapp oscillator topology and to verify it experimentally via microstrip technology. No circuit equations, state-space models, bifurcation analysis, Lyapunov exponents, parameter values, numerical integrations, or self-citations appear in the supplied text. Without any claimed derivation, fitted parameters, or uniqueness theorems, there are no steps that can reduce to inputs by construction. The work is therefore self-contained as a proposal rather than a mathematical result, yielding zero circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated premise that the standard Clapp circuit equations admit chaotic solutions under some tuning.

pith-pipeline@v0.9.0 · 5384 in / 1125 out tokens · 45337 ms · 2026-05-14T21:42:45.032221+00:00 · methodology

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Reference graph

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